Finite Group Databasebeta

← Group #13167042

Character table — Group #13167042

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444488888888888888889999121212121212121212121212181818181818242424242424242424242424363636363636545454545454545472727272
order1222344666333366666666666612123666121212121212121212121212222244441212121212121212446666121212121212121212121212444412128888888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ511111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1
χ611111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ711111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ811111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-111
χ91-11-111-1-1-111111-1-1-1-1-1-1-11111-11-11-1-111-1111-1-1-111-1-111-1-11-11-111-1-111-1-11-111-1-1111-1-1-1111-1-1-1i−ii−i1-1ii−i−iii−i−ii−ii−i
χ101-11-111-1-1-111111-1-1-1-1-1-1-11111-11-11-1-111-1111-1-1-111-1-111-1-11-11-111-1-111-1-11-111-1-1111-1-1-1111-1-1-1−ii−ii1-1−i−iii−i−iii−ii−ii
χ111-11-111-1-1-111111-1-1-1-1-1-1-11111-11-11-1-111-1111-1-1-111-1-111-1-1-11-11-1-111-1-1111-111-1-1-1-1-1111-1-1-1111i−ii−i1-1−i−iii−i−iiii−ii−i
χ121-11-111-1-1-111111-1-1-1-1-1-1-11111-11-11-1-111-1111-1-1-111-1-111-1-1-11-11-1-111-1-1111-111-1-1-1-1-1111-1-1-1111−ii−ii1-1ii−i−iii−i−i−ii−ii
χ131-11-11-11-1-111111-1-1-1-1-1-1-11111-1-111-1-11-11-1-1-1111-1-111-1-1111-1-1111-1-1-1-1111-1-1-111111-1-1-1-1-1-1111i−i−ii1-1ii−i−i−i−iiii−i−ii
χ141-11-11-11-1-111111-1-1-1-1-1-1-11111-1-111-1-11-11-1-1-1111-1-111-1-1111-1-1111-1-1-1-1111-1-1-111111-1-1-1-1-1-1111−iii−i1-1−i−iiiii−i−i−iii−i
χ151-11-11-11-1-111111-1-1-1-1-1-1-11111-1-111-1-11-11-1-1-1111-1-111-1-111-111-1-1-11111-1-11-1-1-111-1-1-1111111-1-1-1i−i−ii1-1−i−iiiii−i−ii−i−ii
χ161-11-11-11-1-111111-1-1-1-1-1-1-11111-1-111-1-11-11-1-1-1111-1-111-1-111-111-1-1-11111-1-11-1-1-111-1-1-1111111-1-1-1−iii−i1-1ii−i−i−i−iii−iii−i
χ1722222222222222222222222222222222222222222222-2-2-2-2000000000000-2-2-2-2-2-20000000000000000-2-2000000000000
χ1822222-2-22222222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000-2-222220000000000000000-2-2000000000000
χ192222-122-1-1-122-1-1222-1-1-1-122-1-12-1-1-1-1-1-1222-1-12-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-12-1-12-1-12-1-12-1-10000-1-1000000000000
χ202222-122-1-1-122-1-1222-1-1-1-122-1-12-1-1-1-1-1-1222-1-12-1-1-1-1-1-12222-2-2-2-21111111122-1-1-1-1-211-211-211-2110000-1-1000000000000
χ212222-122-1-1-122-1-1222-1-1-1-122-1-12-1-1-1-1-1-1222-1-12-1-1-1-1-1-1-2-2-2-20000−i3i3−i3i3−i3i3−i3i3-2-211110−i3i30−i3i30−i3i30−i3i3000011000000000000
χ222222-122-1-1-122-1-1222-1-1-1-122-1-12-1-1-1-1-1-1222-1-12-1-1-1-1-1-1-2-2-2-20000i3−i3i3−i3i3−i3i3−i3-2-211110i3−i30i3−i30i3−i30i3−i3000011000000000000
χ232222-1-2-2-1-1-122-1-1222-1-1-1-122-1-1211-1-1-1-1-2-2-211-211111122220000−i3i3−i3i3i3−i3i3−i3-2-2-1-1-1-10−i3i30−i3i30i3−i30i3−i3000011000000000000
χ242222-1-2-2-1-1-122-1-1222-1-1-1-122-1-1211-1-1-1-1-2-2-211-211111122220000i3−i3i3−i3−i3i3−i3i3-2-2-1-1-1-10i3−i30i3−i30−i3i30−i3i3000011000000000000
χ252222-1-2-2-1-1-122-1-1222-1-1-1-122-1-1211-1-1-1-1-2-2-211-2111111-2-2-2-222-2-2-1-1-1-111112211112-1-12-1-1-211-2110000-1-1000000000000
χ262222-1-2-2-1-1-122-1-1222-1-1-1-122-1-1211-1-1-1-1-2-2-211-2111111-2-2-2-2-2-2221111-1-1-1-1221111-211-2112-1-12-1-10000-1-1000000000000
χ2722-2-22002-2-2222222-222-2-2-2-2-2-2-20022-2-20000000000002-22-2000000000000002-22-20000000000000000002−22−22−22−20000
χ2822-2-22002-2-2222222-222-2-2-2-2-2-2-20022-2-20000000000002-22-2000000000000002-22-2000000000000000000−22−22−22−220000
χ2922-2-22002-2-2222222-222-2-2-2-2-2-2-20022-2-2000000000000-22-2200000000000000-22-220000000000000000002−22−2−22−220000
χ3022-2-22002-2-2222222-222-2-2-2-2-2-2-20022-2-2000000000000-22-2200000000000000-22-22000000000000000000−22−222−22−20000
χ312-22-222-2-2-222222-2-2-2-2-2-2-22222-22-22-2-222-2222-2-2-222-2-2-2-222000000000000-22-2-2220000000000000000-22000000000000
χ322-22-22-22-2-222222-2-2-2-2-2-2-22222-2-222-2-22-22-2-2-2222-2-22222-2-2000000000000-2222-2-20000000000000000-22000000000000
χ332-22-2-12-211-122-1-1-2-2-2111122-1-1-2-11-111-12-22-1-1-211-1-11122-2-22-22-2-1-111-1-1112-2-1-1112-1-1-2112-1-1-2110000-11000000000000
χ342-22-2-12-211-122-1-1-2-2-2111122-1-1-2-11-111-12-22-1-1-211-1-11122-2-2-22-2211-1-111-1-12-2-1-111-2112-1-1-2112-1-10000-11000000000000
χ352-22-2-12-211-122-1-1-2-2-2111122-1-1-2-11-111-12-22-1-1-211-1-111-2-2220000−i3i3i3−i3−i3i3i3−i3-2211-1-10−i3i30i3−i30−i3i30i3−i300001-1000000000000
χ362-22-2-12-211-122-1-1-2-2-2111122-1-1-2-11-111-12-22-1-1-211-1-111-2-2220000i3−i3−i3i3i3−i3−i3i3-2211-1-10i3−i30−i3i30i3−i30−i3i300001-1000000000000
χ372-22-2-1-2211-122-1-1-2-2-2111122-1-1-21-1-111-1-22-2112-1-111-1-122-2-20000−i3i3i3−i3i3−i3−i3i3-22-1-1110−i3i30i3−i30i3−i30−i3i300001-1000000000000
χ382-22-2-1-2211-122-1-1-2-2-2111122-1-1-21-1-111-1-22-2112-1-111-1-122-2-20000i3−i3−i3i3−i3i3i3−i3-22-1-1110i3−i30−i3i30−i3i30i3−i300001-1000000000000
χ392-22-2-1-2211-122-1-1-2-2-2111122-1-1-21-1-111-1-22-2112-1-111-1-1-2-2222-2-22-1-11111-1-12-211-1-12-1-1-211-2112-1-10000-11000000000000
χ402-22-2-1-2211-122-1-1-2-2-2111122-1-1-21-1-111-1-22-2112-1-111-1-1-2-222-222-211-1-1-1-1112-211-1-1-2112-1-12-1-1-2110000-11000000000000
χ412-2-22200-22-22222-2-22-2-222-2-2-2-22002-22-20000000000002-2-22000000000000002-2-22000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ422-2-22200-22-22222-2-22-2-222-2-2-2-22002-22-20000000000002-2-22000000000000002-2-22000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ432-2-22200-22-22222-2-22-2-222-2-2-2-22002-22-2000000000000-222-200000000000000-222-2000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ442-2-22200-22-22222-2-22-2-222-2-2-2-22002-22-2000000000000-222-200000000000000-222-2000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ4544444444441-2111-211111-2111-244-2-2-2-2-2-2111111-2-2-2-20000222222222222000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ4644444444441-2111-211111-2111-244-2-2-2-2-2-2111111-2-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-2000000111111111111000000000000000000
χ474444444444-21-2-2-21-2-2-2-2-21-2-2-2144111111-2-2-2-2-2-21111000000000000000000000000000000000022220000000000-1-1-1-1
χ484444444444-21-2-2-21-2-2-2-2-21-2-2-2144111111-2-2-2-2-2-211110000000000000000000000000000000000-2-2-2-200000000001111
χ4944444-4-44441-2111-211111-2111-2-4-4-2-2-2-222-1-1-1-1-1-12222000022-2-22222-2-2-2-2000000-1-1-1-1-1-1111111000000000000000000
χ5044444-4-44441-2111-211111-2111-2-4-4-2-2-2-222-1-1-1-1-1-122220000-2-222-2-2-2-22222000000111111-1-1-1-1-1-1000000000000000000
χ5144444-4-4444-21-2-2-21-2-2-2-2-21-2-2-21-4-41111-1-1222222-1-1-1-1000000000000000000000000000000000022-2-20000000000-1-111
χ5244444-4-4444-21-2-2-21-2-2-2-2-21-2-2-21-4-41111-1-1222222-1-1-1-10000000000000000000000000000000000-2-222000000000011-1-1
χ534444-244-2-2-21-2−1−3i32−1+3i321-21−1−3i32−1+3i32−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-21111-2-21−1−3i32−1+3i321−1−3i32−1+3i32111100002222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32000000000000000000
χ544444-244-2-2-21-2−1−3i32−1+3i321-21−1−3i32−1+3i32−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-21111-2-21−1−3i32−1+3i321−1−3i32−1+3i3211110000-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i30000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ554444-244-2-2-21-2−1+3i32−1−3i321-21−1+3i32−1−3i32−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-21111-2-21−1+3i32−1−3i321−1+3i32−1−3i32111100002222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32000000000000000000
χ564444-244-2-2-21-2−1+3i32−1−3i321-21−1+3i32−1−3i32−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-21111-2-21−1+3i32−1−3i321−1+3i32−1−3i3211110000-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i30000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ574444-2-4-4-2-2-21-2−1−3i32−1+3i321-21−1−3i32−1+3i32−1−3i32−1+3i32-21−1−3i32−1+3i32-222111122-11+3i321−3i32-11+3i321−3i32-1-1-1-1000022-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ584444-2-4-4-2-2-21-2−1−3i32−1+3i321-21−1−3i32−1+3i32−1−3i32−1+3i32-21−1−3i32−1+3i32-222111122-11+3i321−3i32-11+3i321−3i32-1-1-1-10000-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i30000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32000000000000000000
χ594444-2-4-4-2-2-21-2−1+3i32−1−3i321-21−1+3i32−1−3i32−1+3i32−1−3i32-21−1+3i32−1−3i32-222111122-11−3i321+3i32-11−3i321+3i32-1-1-1-1000022-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3000000-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ604444-2-4-4-2-2-21-2−1+3i32−1−3i321-21−1+3i32−1−3i32−1+3i32−1−3i32-21−1+3i32−1−3i32-222111122-11−3i321+3i32-11−3i321+3i32-1-1-1-10000-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i30000001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32000000000000000000
χ6144-4-4-200-22244-2-244-4-2-222-4-422-400-2-2220000000000004-44-400000000000000-22-22000000000000000000000000000000
χ6244-4-4-200-22244-2-244-4-2-222-4-422-400-2-222000000000000-44-44000000000000002-22-2000000000000000000000000000000
χ634-44-444-4-4-441-211-12-1-1-1-1-1-211124-4-222-2-22111-1-1-1-2-22200002-22-222-2-222-2-2000000-1-1-1111-1-1-1111000000000000000000
χ644-44-444-4-4-441-211-12-1-1-1-1-1-211124-4-222-2-22111-1-1-1-2-2220000-22-22-2-222-2-222000000111-1-1-1111-1-1-1000000000000000000
χ654-44-444-4-4-44-21-2-22-1222221-2-2-2-14-41-1-111-1-2-2-222211-1-100000000000000000000000000000000002i−2i2i−2i0000000000−ii−ii
χ664-44-444-4-4-44-21-2-22-1222221-2-2-2-14-41-1-111-1-2-2-222211-1-10000000000000000000000000000000000−2i2i−2i2i0000000000i−ii−i
χ674-44-44-44-4-441-211-12-1-1-1-1-1-21112-44-222-22-2-1-1-111122-2-200002-2-2222-2-2-2-222000000-1-1-1111111-1-1-1000000000000000000
χ684-44-44-44-4-441-211-12-1-1-1-1-1-21112-44-222-22-2-1-1-111122-2-20000-222-2-2-22222-2-2000000111-1-1-1-1-1-1111000000000000000000
χ694-44-44-44-4-44-21-2-22-1222221-2-2-2-1-441-1-11-11222-2-2-2-1-11100000000000000000000000000000000002i−2i−2i2i0000000000−iii−i
χ704-44-44-44-4-44-21-2-22-1222221-2-2-2-1-441-1-11-11222-2-2-2-1-1110000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii
χ714-44-4-24-422-21-2−1−3i32−1+3i32-12-11+3i321−3i321+3i321−3i32-21−1−3i32−1+3i322-221-1-11-221−1−3i32−1+3i32-11+3i321−3i3211-1-100002-22-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3000000-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i32000000000000000000
χ724-44-4-24-422-21-2−1−3i32−1+3i32-12-11+3i321−3i321+3i321−3i32-21−1−3i32−1+3i322-221-1-11-221−1−3i32−1+3i32-11+3i321−3i3211-1-10000-22-221+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i30000001−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i32000000000000000000
χ734-44-4-24-422-21-2−1+3i32−1−3i32-12-11−3i321+3i321−3i321+3i32-21−1+3i32−1−3i322-221-1-11-221−1+3i32−1−3i32-11−3i321+3i3211-1-100002-22-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i3000000-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i32000000000000000000
χ744-44-4-24-422-21-2−1+3i32−1−3i32-12-11−3i321+3i321−3i321+3i32-21−1+3i32−1−3i322-221-1-11-221−1+3i32−1−3i32-11−3i321+3i3211-1-10000-22-221−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i30000001−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i32000000000000000000
χ754-44-4-2-4422-21-2−1−3i32−1+3i32-12-11+3i321−3i321+3i321−3i32-21−1−3i32−1+3i3222-21-1-112-2-11+3i321−3i321−1−3i32−1+3i32-1-11100002-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3000000-11+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32000000000000000000
χ764-44-4-2-4422-21-2−1−3i32−1+3i32-12-11+3i321−3i321+3i321−3i32-21−1−3i32−1+3i3222-21-1-112-2-11+3i321−3i321−1−3i32−1+3i32-1-1110000-222-21+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i30000001−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i32000000000000000000
χ774-44-4-2-4422-21-2−1+3i32−1−3i32-12-11−3i321+3i321−3i321+3i32-21−1+3i32−1−3i3222-21-1-112-2-11−3i321+3i321−1+3i32−1−3i32-1-11100002-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3000000-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32000000000000000000
χ784-44-4-2-4422-21-2−1+3i32−1−3i32-12-11−3i321+3i321−3i321+3i32-21−1+3i32−1−3i3222-21-1-112-2-11−3i321+3i321−1+3i32−1−3i32-1-1110000-222-21−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i30000001−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i32000000000000000000
χ794-4-44-2002-2244-2-2-4-4422-2-2-4-422400-22-220000000000004-4-4400000000000000-222-2000000000000000000000000000000
χ804-4-44-2002-2244-2-2-4-4422-2-2-4-422400-22-22000000000000-444-4000000000000002-2-22000000000000000000000000000000
χ818888-488-4-4-4-4222-42-422222-4222-4-4-1-1-1-122-422-422-1-1-1-10000000000000000000000000000000000000000000000000000
χ828888-4-8-8-4-4-4-4222-42-422222-422244-1-1-1-1-2-24-2-24-2-211110000000000000000000000000000000000000000000000000000
χ8388-8-88008-8-82-4222-4-222-2-24-2-2-2400-4-4440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88008-8-8-42-4-4-424-4-444-2444-20022-2-20000000000000000000000000000000000000000000000000000000000000000
χ8588-8-8-400-4442-4−1−3i3−1+3i32-4-2−1−3i3−1+3i31+3i31−3i34-21+3i31−3i340022-2-20000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-400-4442-4−1+3i3−1−3i32-4-2−1+3i3−1−3i31−3i31+3i34-21−3i31+3i340022-2-20000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-400-444-4222-42422-2-2-24-2-2-200-1-1110000000033−3333−330000000000000000000000000000000000000000000000000000
χ8888-8-8-400-444-4222-42422-2-2-24-2-2-200-1-11100000000−3333−33330000000000000000000000000000000000000000000000000000
χ898-88-8-48-844-4-42224-24-2-2-2-22-422-2-44-111-12-2-4224-2-2-1-1110000000000000000000000000000000000000000000000000000
χ908-88-8-4-8844-4-42224-24-2-2-2-22-422-24-4-111-1-224-2-2-42211-1-10000000000000000000000000000000000000000000000000000
χ918-8-88800-88-82-422-242-2-2224-2-2-2-400-44-440000000000000000000000000000000000000000000000000000000000000000
χ928-8-88800-88-8-42-4-44-2-444-4-4-24442002-22-20000000000000000000000000000000000000000000000000000000000000000
χ938-8-88-4004-442-4−1−3i3−1+3i3-2421+3i31−3i3−1−3i3−1+3i34-21+3i31−3i3-4002-22-20000000000000000000000000000000000000000000000000000000000000000
χ948-8-88-4004-442-4−1+3i3−1−3i3-2421−3i31+3i3−1+3i3−1−3i34-21−3i31+3i3-4002-22-20000000000000000000000000000000000000000000000000000000000000000
χ958-8-88-4004-44-42224-2-4-2-222-24-2-2200-11-110000000033−33−33330000000000000000000000000000000000000000000000000000
χ968-8-88-4004-44-42224-2-4-2-222-24-2-2200-11-1100000000−333333−330000000000000000000000000000000000000000000000000000

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