Finite Group Databasebeta

← Group #13181116

Character table — Group #13181116

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112224444444448888888899121212121212181818242424242424363636545454547272112224444444448888888899121212121212181818242424242424363636545454547272
order122363333666663666666644246612124121266612121224128888612222666666666666666666644246612124121266612121224128888612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-11-1-1-1-1-1-1111111111111111111111111111111111111111-1-11-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-111111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-111
χ4111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1
χ511-1111111-111111-1-1-1-11-1-1-1-11-111-1-11-1-1111-1-1-11-1111-1-11-111-1111111-111111-1-1-1-11-1-1-1-11-111-1-11-1-1111-1-1-11-1111-1-11-1
χ611-1111111-111111-1-1-1-11-1-1-1-11-111-1-11-1-1111-1-1-1-111-1-111-1111-1111111-111111-1-1-1-11-1-1-1-11-111-1-11-1-1111-1-1-1-111-1-111-11
χ711-1111111-111111-1-1-1-11-1-1-1-1-11-1-1111-1-1-1-1-11111-11-1-1111-111-1111111-111111-1-1-1-11-1-1-1-1-11-1-1111-1-1-1-1-11111-11-1-1111-1
χ811-1111111-111111-1-1-1-11-1-1-1-1-11-1-1111-1-1-1-1-1111-11111-1-1-1111-1111111-111111-1-1-1-11-1-1-1-1-11-1-1111-1-1-1-1-1111-11111-1-1-11
χ92222222222222222222222-2-2000000-2-2-200000000-20000002222222222222222222222-2-2000000-2-2-200000000-2000000
χ10222-1-12-1-12-12-1-12-12-1-12-1-1-12222-1-1-1-12-1-12-1-12-1-100-1000000222-1-12-1-12-12-1-12-12-1-12-1-1-12222-1-1-1-12-1-12-1-12-1-100-1000000
χ11222-1-12-1-12-12-1-12-12-1-12-1-1-122-2-211112-1-1-211-21100-1000000222-1-12-1-12-12-1-12-12-1-12-1-1-122-2-211112-1-1-211-21100-1000000
χ12222-1-12-1-12-12-1-12-12-1-12-1-1-1-2-200−i3i3−i3i3-2110−i3i30−i3i3001000000222-1-12-1-12-12-1-12-12-1-12-1-1-1-2-200−i3i3−i3i3-2110−i3i30−i3i3001000000
χ13222-1-12-1-12-12-1-12-12-1-12-1-1-1-2-200i3−i3i3−i3-2110i3−i30i3−i3001000000222-1-12-1-12-12-1-12-12-1-12-1-1-1-2-200i3−i3i3−i3-2110i3−i30i3−i3001000000
χ1422-2222222-222222-2-2-2-22-2-222000000-22200000000-200000022-2222222-222222-2-2-2-22-2-222000000-22200000000-2000000
χ1522-2-1-12-1-1212-1-12-1-211-2-1112200−i3i3i3−i3-2-1-10−i3i30i3−i300100000022-2-1-12-1-1212-1-12-1-211-2-1112200−i3i3i3−i3-2-1-10−i3i30i3−i3001000000
χ1622-2-1-12-1-1212-1-12-1-211-2-1112200i3−i3−i3i3-2-1-10i3−i30−i3i300100000022-2-1-12-1-1212-1-12-1-211-2-1112200i3−i3−i3i3-2-1-10i3−i30−i3i3001000000
χ1722-2-1-12-1-1212-1-12-1-211-2-111-2-22-2-1-1112112-1-1-21100-100000022-2-1-12-1-1212-1-12-1-211-2-111-2-22-2-1-1112112-1-1-21100-1000000
χ1822-2-1-12-1-1212-1-12-1-211-2-111-2-2-2211-1-1211-2112-1-100-100000022-2-1-12-1-1212-1-12-1-211-2-111-2-2-2211-1-1211-2112-1-100-1000000
χ192-202-222220-2-2-2-220000-2002i−2i00000002i−2i0000000002−2−i2i2002-202-222220-2-2-2-220000-2002i−2i00000002i−2i0000000002−2−i2i200
χ202-202-222220-2-2-2-220000-2002i−2i00000002i−2i000000000−22i2−i2002-202-222220-2-2-2-220000-2002i−2i00000002i−2i000000000−22i2−i200
χ212-202-222220-2-2-2-220000-200−2i2i0000000−2i2i0000000002−2i2−i2002-202-222220-2-2-2-220000-200−2i2i0000000−2i2i0000000002−2i2−i200
χ222-202-222220-2-2-2-220000-200−2i2i0000000−2i2i000000000−22−i2i2002-202-222220-2-2-2-220000-200−2i2i0000000−2i2i000000000−22−i2i200
χ2344444111-24111-2-2111-2-2-2-200222222000-1-1-1-1-1-100000000044444111-24111-2-2111-2-2-2-200222222000-1-1-1-1-1-1000000000
χ2444444111-24111-2-2111-2-2-2-200-2-2-2-2-2-200011111100000000044444111-24111-2-2111-2-2-2-200-2-2-2-2-2-2000111111000000000
χ2544444-2-2-214-2-2-211-2-2-21111000000000000000002200000-1-144444-2-2-214-2-2-211-2-2-21111000000000000000002200000-1-1
χ2644444-2-2-214-2-2-211-2-2-2111100000000000000000-2-2000001144444-2-2-214-2-2-211-2-2-2111100000000000000000-2-20000011
χ27444-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32-21110022−1−i3−1+i3−1−i3−1+i3000-11+i321−i32-11+i321−i32000000000444-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32-21110022−1−i3−1+i3−1−i3−1+i3000-11+i321−i32-11+i321−i32000000000
χ28444-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32-211100-2-21+i31−i31+i31−i30001−1−i32−1+i321−1−i32−1+i32000000000444-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32-211100-2-21+i31−i31+i31−i30001−1−i32−1+i321−1−i32−1+i32000000000
χ29444-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32-21110022−1+i3−1−i3−1+i3−1−i3000-11−i321+i32-11−i321+i32000000000444-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32-21110022−1+i3−1−i3−1+i3−1−i3000-11−i321+i32-11−i321+i32000000000
χ30444-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32-211100-2-21−i31+i31−i31+i30001−1+i32−1−i321−1+i32−1−i32000000000444-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32-211100-2-21−i31+i31−i31+i30001−1+i32−1−i321−1+i32−1−i32000000000
χ3144-444111-2-4111-2-2-1-1-12-222002-222-2-2000-1-1-111100000000044-444111-2-4111-2-2-1-1-12-222002-222-2-2000-1-1-1111000000000
χ3244-444111-2-4111-2-2-1-1-12-22200-22-2-222000111-1-1-100000000044-444111-2-4111-2-2-1-1-12-22200-22-2-222000111-1-1-1000000000
χ3344-444-2-2-21-4-2-2-211222-11-1-1000000000000000002-200000-1144-444-2-2-21-4-2-2-211222-11-1-1000000000000000002-200000-11
χ3444-444-2-2-21-4-2-2-211222-11-1-100000000000000000-22000001-144-444-2-2-21-4-2-2-211222-11-1-100000000000000000-22000001-1
χ3544-4-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-21-11+3i321−3i3221-1-1002-2−1−i3−1+i31+i31−i3000-11+i321−i321−1−i32−1+i3200000000044-4-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-21-11+3i321−3i3221-1-1002-2−1−i3−1+i31+i31−i3000-11+i321−i321−1−i32−1+i32000000000
χ3644-4-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-21-11+3i321−3i3221-1-100-221+i31−i3−1−i3−1+i30001−1−i32−1+i32-11+i321−i3200000000044-4-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-21-11+3i321−3i3221-1-100-221+i31−i3−1−i3−1+i30001−1−i32−1+i32-11+i321−i32000000000
χ3744-4-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-21-11−3i321+3i3221-1-1002-2−1+i3−1−i31−i31+i3000-11−i321+i321−1+i32−1−i3200000000044-4-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-21-11−3i321+3i3221-1-1002-2−1+i3−1−i31−i31+i3000-11−i321+i321−1+i32−1−i32000000000
χ3844-4-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-21-11−3i321+3i3221-1-100-221−i31+i3−1+i3−1−i30001−1+i32−1−i32-11−i321+i3200000000044-4-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-21-11−3i321+3i3221-1-100-221−i31+i3−1+i3−1−i30001−1+i32−1−i32-11−i321+i32000000000
χ394-40-224-2-240-422-4-200002004i−4i0000000−2i2i0000000000000004-40-224-2-240-422-4-200002004i−4i0000000−2i2i000000000000000
χ404-40-224-2-240-422-4-20000200−4i4i00000002i−2i0000000000000004-40-224-2-240-422-4-20000200−4i4i00000002i−2i000000000000000
χ41888-4-4-4222-4-4222-1-4222-1-1-100000000000000000000000000888-4-4-4222-4-4222-1-4222-1-1-100000000000000000000000000
χ4288-8-4-4-42224-4222-14-2-2-2-1110000000000000000000000000088-8-4-4-42224-4222-14-2-2-2-11100000000000000000000000000
χ438-808-8222-40-2-2-24-40000400000000000000000000000000008-808-8222-40-2-2-24-4000040000000000000000000000000000
χ448-808-8-4-4-420444-220000-200000000000000000000000000008-808-8-4-4-420444-220000-20000000000000000000000000000
χ458-80-442−1−3i3−1+3i3-40-21+3i31−3i3420000-200000000000000000000000000008-80-442−1−3i3−1+3i3-40-21+3i31−3i3420000-20000000000000000000000000000
χ468-80-442−1+3i3−1−3i3-40-21−3i31+3i3420000-200000000000000000000000000008-80-442−1+3i3−1−3i3-40-21−3i31+3i3420000-20000000000000000000000000000
χ478-80-44-422204-2-2-2-100001−3i33i3000000000000000000000000008-80-44-422204-2-2-2-100001−3i33i300000000000000000000000000
χ488-80-44-422204-2-2-2-1000013i3−3i3000000000000000000000000008-80-44-422204-2-2-2-1000013i3−3i300000000000000000000000000
χ49111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ50111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ51111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111111-1-1-11111-1-1
χ52111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111111111-1-1-1-1-111
χ5311-1111111-111111-1-1-1-11-1-1-1-11-111-1-11-1-1111-1-1-11-1111-1-11-1-1-11-1-1-1-1-1-11-1-1-1-1-11111-11111-11-1-111-111-1-1-1111-11-1-1-111-11
χ5411-1111111-111111-1-1-1-11-1-1-1-11-111-1-11-1-1111-1-1-1-111-1-111-11-1-11-1-1-1-1-1-11-1-1-1-1-11111-11111-11-1-111-111-1-1-11111-1-111-1-11-1
χ5511-1111111-111111-1-1-1-11-1-1-1-1-11-1-1111-1-1-1-1-11111-11-1-1111-1-1-11-1-1-1-1-1-11-1-1-1-1-11111-111111-111-1-1-111111-1-1-1-11-111-1-1-11
χ5611-1111111-111111-1-1-1-11-1-1-1-1-11-1-1111-1-1-1-1-1111-11111-1-1-11-1-11-1-1-1-1-1-11-1-1-1-1-11111-111111-111-1-1-111111-1-1-11-1-1-1-1111-1
χ572222222222222222222222-2-2000000-2-2-200000000-2000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222000000222000000002000000
χ58222-1-12-1-12-12-1-12-12-1-12-1-1-12222-1-1-1-12-1-12-1-12-1-100-1000000-2-2-211-211-21-211-21-211-2111-2-2-2-21111-211-211-211001000000
χ59222-1-12-1-12-12-1-12-12-1-12-1-1-122-2-211112-1-1-211-21100-1000000-2-2-211-211-21-211-21-211-2111-2-222-1-1-1-1-2112-1-12-1-1001000000
χ60222-1-12-1-12-12-1-12-12-1-12-1-1-1-2-200−i3i3−i3i3-2110−i3i30−i3i3001000000-2-2-211-211-21-211-21-211-21112200i3−i3i3−i32-1-10i3−i30i3−i300-1000000
χ61222-1-12-1-12-12-1-12-12-1-12-1-1-1-2-200i3−i3i3−i3-2110i3−i30i3−i3001000000-2-2-211-211-21-211-21-211-21112200−i3i3−i3i32-1-10−i3i30−i3i300-1000000
χ6222-2222222-222222-2-2-2-22-2-222000000-22200000000-2000000-2-22-2-2-2-2-2-22-2-2-2-2-22222-222-2-20000002-2-2000000002000000
χ6322-2-1-12-1-1212-1-12-1-211-2-1112200−i3i3i3−i3-2-1-10−i3i30i3−i3001000000-2-2211-211-2-1-211-212-1-121-1-1-2-200i3−i3−i3i32110i3−i30−i3i300-1000000
χ6422-2-1-12-1-1212-1-12-1-211-2-1112200i3−i3−i3i3-2-1-10i3−i30−i3i3001000000-2-2211-211-2-1-211-212-1-121-1-1-2-200−i3i3i3−i32110−i3i30i3−i300-1000000
χ6522-2-1-12-1-1212-1-12-1-211-2-111-2-22-2-1-1112112-1-1-21100-1000000-2-2211-211-2-1-211-212-1-121-1-122-2211-1-1-2-1-1-2112-1-1001000000
χ6622-2-1-12-1-1212-1-12-1-211-2-111-2-2-2211-1-1211-2112-1-100-1000000-2-2211-211-2-1-211-212-1-121-1-1222-2-1-111-2-1-12-1-1-211001000000
χ672-202-222220-2-2-2-220000-2002i−2i00000002i−2i0000000002−2−i2i200-220-22-2-2-2-202222-20000200−2i2i0000000−2i2i000000000−22i2−i200
χ682-202-222220-2-2-2-220000-2002i−2i00000002i−2i000000000−22i2−i200-220-22-2-2-2-202222-20000200−2i2i0000000−2i2i0000000002−2−i2i200
χ692-202-222220-2-2-2-220000-200−2i2i0000000−2i2i0000000002−2i2−i200-220-22-2-2-2-202222-200002002i−2i00000002i−2i000000000−22−i2i200
χ702-202-222220-2-2-2-220000-200−2i2i0000000−2i2i000000000−22−i2i200-220-22-2-2-2-202222-200002002i−2i00000002i−2i0000000002−2i2−i200
χ7144444111-24111-2-2111-2-2-2-200222222000-1-1-1-1-1-1000000000-4-4-4-4-4-1-1-12-4-1-1-122-1-1-1222200-2-2-2-2-2-2000111111000000000
χ7244444111-24111-2-2111-2-2-2-200-2-2-2-2-2-2000111111000000000-4-4-4-4-4-1-1-12-4-1-1-122-1-1-1222200222222000-1-1-1-1-1-1000000000
χ7344444-2-2-214-2-2-211-2-2-21111000000000000000002200000-1-1-4-4-4-4-4222-1-4222-1-1222-1-1-1-100000000000000000-2-20000011
χ7444444-2-2-214-2-2-211-2-2-2111100000000000000000-2-20000011-4-4-4-4-4222-1-4222-1-1222-1-1-1-1000000000000000002200000-1-1
χ75444-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32-21110022−1−i3−1+i3−1−i3−1+i3000-11+i321−i32-11+i321−i32000000000-4-4-422-11+3i321−3i3222-11+3i321−3i322-1-11+3i321−3i322-1-1-100-2-21+i31−i31+i31−i30001−1−i32−1+i321−1−i32−1+i32000000000
χ76444-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32-211100-2-21+i31−i31+i31−i30001−1−i32−1+i321−1−i32−1+i32000000000-4-4-422-11+3i321−3i3222-11+3i321−3i322-1-11+3i321−3i322-1-1-10022−1−i3−1+i3−1−i3−1+i3000-11+i321−i32-11+i321−i32000000000
χ77444-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32-21110022−1+i3−1−i3−1+i3−1−i3000-11−i321+i32-11−i321+i32000000000-4-4-422-11−3i321+3i3222-11−3i321+3i322-1-11−3i321+3i322-1-1-100-2-21−i31+i31−i31+i30001−1+i32−1−i321−1+i32−1−i32000000000
χ78444-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32-211100-2-21−i31+i31−i31+i30001−1+i32−1−i321−1+i32−1−i32000000000-4-4-422-11−3i321+3i3222-11−3i321+3i322-1-11−3i321+3i322-1-1-10022−1+i3−1−i3−1+i3−1−i3000-11−i321+i32-11−i321+i32000000000
χ7944-444111-2-4111-2-2-1-1-12-222002-222-2-2000-1-1-1111000000000-4-44-4-4-1-1-124-1-1-122111-22-2-200-22-2-222000111-1-1-1000000000
χ8044-444111-2-4111-2-2-1-1-12-22200-22-2-222000111-1-1-1000000000-4-44-4-4-1-1-124-1-1-122111-22-2-2002-222-2-2000-1-1-1111000000000
χ8144-444-2-2-21-4-2-2-211222-11-1-1000000000000000002-200000-11-4-44-4-4222-14222-1-1-2-2-21-11100000000000000000-22000001-1
χ8244-444-2-2-21-4-2-2-211222-11-1-100000000000000000-22000001-1-4-44-4-4222-14222-1-1-2-2-21-111000000000000000002-200000-11
χ8344-4-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-21-11+3i321−3i3221-1-1002-2−1−i3−1+i31+i31−i3000-11+i321−i321−1−i32−1+i32000000000-4-4422-11+3i321−3i322-2-11+3i321−3i322-11−1−3i32−1+3i32-2-11100-221+i31−i3−1−i3−1+i30001−1−i32−1+i32-11+i321−i32000000000
χ8444-4-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-21-11+3i321−3i3221-1-100-221+i31−i3−1−i3−1+i30001−1−i32−1+i32-11+i321−i32000000000-4-4422-11+3i321−3i322-2-11+3i321−3i322-11−1−3i32−1+3i32-2-111002-2−1−i3−1+i31+i31−i3000-11+i321−i321−1−i32−1+i32000000000
χ8544-4-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-21-11−3i321+3i3221-1-1002-2−1+i3−1−i31−i31+i3000-11−i321+i321−1+i32−1−i32000000000-4-4422-11−3i321+3i322-2-11−3i321+3i322-11−1+3i32−1−3i32-2-11100-221−i31+i3−1+i3−1−i30001−1+i32−1−i32-11−i321+i32000000000
χ8644-4-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-21-11−3i321+3i3221-1-100-221−i31+i3−1+i3−1−i30001−1+i32−1−i32-11−i321+i32000000000-4-4422-11−3i321+3i322-2-11−3i321+3i322-11−1+3i32−1−3i32-2-111002-2−1+i3−1−i31−i31+i3000-11−i321+i321−1+i32−1−i32000000000
χ874-40-224-2-240-422-4-200002004i−4i0000000−2i2i000000000000000-4402-2-422-404-2-2420000-200−4i4i00000002i−2i000000000000000
χ884-40-224-2-240-422-4-20000200−4i4i00000002i−2i000000000000000-4402-2-422-404-2-2420000-2004i−4i0000000−2i2i000000000000000
χ89888-4-4-4222-4-4222-1-4222-1-1-100000000000000000000000000-8-8-8444-2-2-244-2-2-214-2-2-211100000000000000000000000000
χ9088-8-4-4-42224-4222-14-2-2-2-11100000000000000000000000000-8-88444-2-2-2-44-2-2-21-42221-1-100000000000000000000000000
χ918-808-8222-40-2-2-24-4000040000000000000000000000000000-880-88-2-2-240222-440000-40000000000000000000000000000
χ928-808-8-4-4-420444-220000-20000000000000000000000000000-880-88444-20-4-4-42-2000020000000000000000000000000000
χ938-80-442−1−3i3−1+3i3-40-21+3i31−3i3420000-20000000000000000000000000000-8804-4-21+3i31−3i3402−1−3i3−1+3i3-4-2000020000000000000000000000000000
χ948-80-442−1+3i3−1−3i3-40-21−3i31+3i3420000-20000000000000000000000000000-8804-4-21−3i31+3i3402−1+3i3−1−3i3-4-2000020000000000000000000000000000
χ958-80-44-422204-2-2-2-100001−3i33i300000000000000000000000000-8804-44-2-2-20-422210000-13i3−3i300000000000000000000000000
χ968-80-44-422204-2-2-2-1000013i3−3i300000000000000000000000000-8804-44-2-2-20-422210000-1−3i33i300000000000000000000000000

Here i is the imaginary unit (i² = −1).