Finite Group Databasebeta

← Group #13167418

Character table — Group #13167418

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444444488888888888888888899991818181818181818181818181818363636363636363636363636363636363636363636363636363672727272
order124423461212336666612121212121212336666666121212121212121212224424668888888812122244444461212121212121212122424242424242424661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ51111-11-111111-1-1-111-11111-1-111-1-1-1-1-111-11111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-11-11-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i1-11-1
χ61111-11-111111-1-1-111-11111-1-111-1-1-1-1-111-11111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-1-11-11−i−iii11−i−i−i−iiiiiiiii−i−i−i−i-11-11
χ71111-11-111111-1-1-111-11111-1-111-1-1-1-1-111-11111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-11-11-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ81111-11-111111-1-1-111-11111-1-111-1-1-1-1-111-11111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-1-11-11ii−i−i11iiii−i−i−i−i−i−i−i−iiiii-11-11
χ911-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-11-1-1ii−i−iii−i−i111-1-11i−ii−i-11ii−i−iii−i−iii−i−iii−i−i1-1-11
χ1011-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-11-1-1ii−i−iii−i−i11-111-1−ii−ii-11−i−iii−i−iiiii−i−iii−i−i-111-1
χ1111-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-11-1-1−i−iii−i−iii111-1-11−ii−ii-11−i−iii−i−iii−i−iii−i−iii1-1-11
χ1211-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-11-1-1−i−iii−i−iii11-111-1i−ii−i-11ii−i−iii−i−i−i−iii−i−iii-111-1
χ1311-1-1-1111-1-111-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-1111111-1-1-111111-1-1-1-111-1-111-1-11-1-11-1111-1-1-1-11111-1-1-1-11111-1-1
χ1411-1-1-1111-1-111-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-1111111-1-1-111111-1-1-1-111-1-1-1-111-111-1-11-1-11111-1-111-1-1-1-111-1-111
χ1511-1-1-1111-1-111-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-1111111-1-1-1111-1-11111-1-1-1-111-1-1-111-1-11-1-11111-1-1-1-11111-1-111-1-1
χ1611-1-1-1111-1-111-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-1111111-1-1-1111-1-11111-1-1-1-1-1-1111-1-11-1111-1-1-1-111-1-11111-1-1-1-111
χ17222222222222222222222222222222222222222222-2-2-2-2-2-2-2-200000000-2-200000000-2-200000000000000000000
χ1822222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1222222-1-100000000-1-100002222-1-1-1-1-1-1-1-1-1-1000000000000
χ1922222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1222222-1-100000000-1-10000-2-2-2-2-1-111111111000000000000
χ2022222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1-2-2-2-2-2-211000000001100000000113−33−33−33−3000000000000
χ2122222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1-2-2-2-2-2-21100000000110000000011−33−33−33−33000000000000
χ222222-22-222222-2-2-222-22222-2-222-2-2-2-2-222-22222-2-2-2-22222-2-222000000002200000000-2-200000000000000000000
χ232222-2-1-2-1-1-1221-2-22212222-2-2-1-1-21111-1-1-2-1-1-1-111112222-2-2-1-100000000-1-10000000011−i3i3−i3i3i3−i3i3−i3000000000000
χ242222-2-1-2-1-1-1221-2-22212222-2-2-1-1-21111-1-1-2-1-1-1-111112222-2-2-1-100000000-1-10000000011i3−i3i3−i3−i3i3−i3i3000000000000
χ252222-2-1-2-1-1-1221-2-22212222-2-2-1-1-21111-1-1-2-1-1-1-11111-2-2-2-22211000000001100002i2i−2i−2i-1-1−i−i−i−iiiii000000000000
χ262222-2-1-2-1-1-1221-2-22212222-2-2-1-1-21111-1-1-2-1-1-1-11111-2-2-2-2221100000000110000−2i−2i2i2i-1-1iiii−i−i−i−i000000000000
χ2722-2-222-22-2-22222222-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-222-2-22-22200000000-2-2000000002-200000000000000000000
χ2822-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-21111111122-2-22-2-1-1000000001100000000-11−i3i3i3−i3−i3i3i3−i3000000000000
χ2922-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-21111111122-2-22-2-1-1000000001100000000-11i3−i3−i3i3i3−i3−i3i3000000000000
χ3022-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-211111111-2-222-221100000000-1-100002i−2i2i−2i1-1−i−iii−i−iii000000000000
χ3122-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-211111111-2-222-221100000000-1-10000−2i2i−2i2i1-1ii−i−iii−i−i000000000000
χ3222-2-2-2222-2-222-2-2-2222-2-2-2-22222-2-2-2-2-2222-2-2-2-22222-2-2222-2-2-20000000022000000002-200000000000000000000
χ3322-2-2-2-12-111221-2-222-1-2-2-2-222-1-1-21111-1-121111-1-1-1-122-2-2-22-1-1000000001100002-2-221-1-1-11111-1-1000000000000
χ3422-2-2-2-12-111221-2-222-1-2-2-2-222-1-1-21111-1-121111-1-1-1-122-2-2-22-1-100000000110000-222-21-111-1-1-1-111000000000000
χ3522-2-2-2-12-111221-2-222-1-2-2-2-222-1-1-21111-1-121111-1-1-1-1-2-2222-21100000000-1-100000000-113−3−33−333−3000000000000
χ3622-2-2-2-12-111221-2-222-1-2-2-2-222-1-1-21111-1-121111-1-1-1-1-2-2222-21100000000-1-100000000-11−333−33−3−33000000000000
χ372-22i−2i020-22i−2i22000-2-202i−2i2i−2i002200000-2-202i2i−2i−2i00002-22i−2i002-22−2−i2i2−i2i22−22i−2i0000000000000000002−2−i2i2−i2i22−20000
χ382-22i−2i020-22i−2i22000-2-202i−2i2i−2i002200000-2-202i2i−2i−2i00002-22i−2i002-2−22i2−i2i2−i2−222i−2i000000000000000000−22i2−i2i2−i2−220000
χ392-22i−2i020-22i−2i22000-2-202i−2i2i−2i002200000-2-202i2i−2i−2i0000-22−2i2i00-22−i2i2−222−2i2−i2−2i2i000000000000000000−i2i2−222−2i2−i20000
χ402-22i−2i020-22i−2i22000-2-202i−2i2i−2i002200000-2-202i2i−2i−2i0000-22−2i2i00-22i2−i22−2−22−i2i2−2i2i000000000000000000i2−i22−2−22−i2i20000
χ412-2−2i2i020-2−2i2i22000-2-20−2i2i−2i2i002200000-2-20−2i−2i2i2i00002-2−2i2i002-22−2i2−i2i2−i22−2−2i2i0000000000000000002−2i2−i2i2−i22−20000
χ422-2−2i2i020-2−2i2i22000-2-20−2i2i−2i2i002200000-2-20−2i−2i2i2i00002-2−2i2i002-2−22−i2i2−i2i2−22−2i2i000000000000000000−22−i2i2−i2i2−220000
χ432-2−2i2i020-2−2i2i22000-2-20−2i2i−2i2i002200000-2-20−2i−2i2i2i0000-222i−2i00-22−i2i22−2−22i2−i22i−2i000000000000000000−i2i22−2−22i2−i20000
χ442-2−2i2i020-2−2i2i22000-2-20−2i2i−2i2i002200000-2-20−2i−2i2i2i0000-222i−2i00-22i2−i2−222−2−i2i22i−2i000000000000000000i2−i2−222−2−i2i20000
χ4544444444441-24111-2411-2-2111-2-211-2-21-2-21-21-211-2-2000000002222222200000000000000000000-1-1-1-1-1-1-1-10000
χ4644444444441-24111-2411-2-2111-2-211-2-21-2-21-21-211-2-200000000-2-2-2-2-2-2-2-200000000000000000000111111110000
χ474444444444-214-2-2-214-2-211-2-2-211-2-211-211-21-21-2-21100000000000000000022220000000000000000000000-1-1-1-1
χ484444444444-214-2-2-214-2-211-2-2-211-2-211-211-21-21-2-211000000000000000000-2-2-2-200000000000000000000001111
χ494444-44-44441-2-4-1-11-2-411-2-2-1-11-22-1-1221-221-21-2-1-122000000002i2i2i2i−2i−2i−2i−2i00000000000000000000−i−i−i−iiiii0000
χ504444-44-44441-2-4-1-11-2-411-2-2-1-11-22-1-1221-221-21-2-1-12200000000−2i−2i−2i−2i2i2i2i2i00000000000000000000iiii−i−i−i−i0000
χ514444-44-4444-21-422-21-4-2-21122-21-122-1-1-21-1-21-2122-1-10000000000000000002-22-20000000000000000000000-11-11
χ524444-44-4444-21-422-21-4-2-21122-21-122-1-1-21-1-21-2122-1-1000000000000000000-22-2200000000000000000000001-11-1
χ5344-4-444-44-4-41-24111-2-4-1-122-1-11-2-211-2-21-22-12-12-1-122000000002i2i−2i−2i2i2i−2i−2i00000000000000000000−i−iii−i−iii0000
χ5444-4-444-44-4-41-24111-2-4-1-122-1-11-2-211-2-21-22-12-12-1-12200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000ii−i−iii−i−i0000
χ5544-4-444-44-4-4-214-2-2-21-422-1-122-211-2-211-21-12-12-122-1-10000000000000000002-2-220000000000000000000000-111-1
χ5644-4-444-44-4-4-214-2-2-21-422-1-122-211-2-211-21-12-12-122-1-1000000000000000000-222-200000000000000000000001-1-11
χ5744-4-4-4444-4-41-2-4-1-11-24-1-122111-22-1-1221-2-2-12-1211-2-20000000022-2-2-2-22200000000000000000000-1-11111-1-10000
χ5844-4-4-4444-4-41-2-4-1-11-24-1-122111-22-1-1221-2-2-12-1211-2-200000000-2-22222-2-20000000000000000000011-1-1-1-1110000
χ5944-4-4-4444-4-4-21-422-21422-1-1-2-2-21-122-1-1-2112-12-1-2-21100000000000000000022-2-20000000000000000000000-1-111
χ6044-4-4-4444-4-4-21-422-21422-1-1-2-2-21-122-1-1-2112-12-1-2-211000000000000000000-2-222000000000000000000000011-1-1
χ614-44i−4i040-44i−4i1-203-3-120i−i−2i2i3i−3i1-203-300-120i−2i−i2i3i−3i00000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ130000
χ624-44i−4i040-44i−4i1-203-3-120i−i−2i2i3i−3i1-203-300-120i−2i−i2i3i−3i0000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ130000
χ634-44i−4i040-44i−4i1-20-33-120i−i−2i2i−3i3i1-20-3300-120i−2i−i2i−3i3i0000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000
χ644-44i−4i040-44i−4i1-20-33-120i−i−2i2i−3i3i1-20-3300-120i−2i−i2i−3i3i00000000002ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000
χ654-44i−4i0-202−2i2i44000-4-404i−4i4i−4i00-2-200000220−2i−2i2i2i00004-44i−4i00-2200000000−2i2i000000000000000000000000000000
χ664-44i−4i0-202−2i2i44000-4-404i−4i4i−4i00-2-200000220−2i−2i2i2i0000-44−4i4i002-2000000002i−2i000000000000000000000000000000
χ674-4−4i4i040-4−4i4i1-203-3-120−ii2i−2i−3i3i1-203-300-120−i2ii−2i−3i3i0000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ230000
χ684-4−4i4i040-4−4i4i1-203-3-120−ii2i−2i−3i3i1-203-300-120−i2ii−2i−3i3i00000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ230000
χ694-4−4i4i040-4−4i4i1-20-33-120−ii2i−2i3i−3i1-20-3300-120−i2ii−2i3i−3i00000000002ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
χ704-4−4i4i040-4−4i4i1-20-33-120−ii2i−2i3i−3i1-20-3300-120−i2ii−2i3i−3i0000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000
χ714-4−4i4i0-2022i−2i44000-4-40−4i4i−4i4i00-2-2000002202i2i−2i−2i00004-4−4i4i00-22000000002i−2i000000000000000000000000000000
χ724-4−4i4i0-2022i−2i44000-4-40−4i4i−4i4i00-2-2000002202i2i−2i−2i0000-444i−4i002-200000000−2i2i000000000000000000000000000000
χ7388888-48-4-4-42-4-4222-4-422-4-422-12-4-1-122-12-4-12-12-1-122000000000000000000000000000000000000000000000000
χ7488888-48-4-4-4-42-4-4-4-42-4-4-422-4-42-1222-1-12-122-12-122-1-1000000000000000000000000000000000000000000000000
χ758888-8-4-8-4-4-42-44-2-22-4422-4-4-2-2-12411-2-2-124-12-1211-2-2000000000000000000000000000000000000000000000000
χ768888-8-4-8-4-4-4-42444-424-4-422442-1-2-2-2112-1-22-12-1-2-211000000000000000000000000000000000000000000000000
χ7788-8-88-4-8-4442-4-4222-44-2-244-2-2-12-4-1-122-1241-21-211-2-2000000000000000000000000000000000000000000000000
χ7888-8-88-4-8-444-42-4-4-4-42444-2-2442-1222-1-12-1-2-21-21-2-211000000000000000000000000000000000000000000000000
χ7988-8-8-8-48-4442-44-2-22-4-4-2-24422-12411-2-2-12-41-21-2-1-122000000000000000000000000000000000000000000000000
χ8088-8-8-8-48-444-42444-42-444-2-2-4-42-1-2-2-2112-12-21-2122-1-1000000000000000000000000000000000000000000000000
χ818-88i−8i080-88i−8i-420004-20−4i4i2i−2i00-42000004-20−4i2i4i−2i0000000000000000000000000000000000000000000000000000
χ828-88i−8i0-404−4i4i2-406-6-2402i−2i−4i4i6i−6i-120-33001-20−i2ii−2i−3i3i00000000000000000000000000000000000000000000000000
χ838-88i−8i0-404−4i4i2-40-66-2402i−2i−4i4i−6i6i-1203-3001-20−i2ii−2i3i−3i00000000000000000000000000000000000000000000000000
χ848-88i−8i0-404−4i4i-420004-20−4i4i2i−2i002-1000−3i33i3-2102i−i−2ii0033−33000000000000000000000000000000000000000000000000
χ858-88i−8i0-404−4i4i-420004-20−4i4i2i−2i002-10003i3−3i3-2102i−i−2ii00−3333000000000000000000000000000000000000000000000000
χ868-8−8i8i080-8−8i8i-420004-204i−4i−2i2i00-42000004-204i−2i−4i2i0000000000000000000000000000000000000000000000000000
χ878-8−8i8i0-4044i−4i2-406-6-240−2i2i4i−4i−6i6i-120-33001-20i−2i−i2i3i−3i00000000000000000000000000000000000000000000000000
χ888-8−8i8i0-4044i−4i2-40-66-240−2i2i4i−4i6i−6i-1203-3001-20i−2i−i2i−3i3i00000000000000000000000000000000000000000000000000
χ898-8−8i8i0-4044i−4i-420004-204i−4i−2i2i002-1000−3i33i3-210−2ii2i−i00−3333000000000000000000000000000000000000000000000000
χ908-8−8i8i0-4044i−4i-420004-204i−4i−2i2i002-10003i3−3i3-210−2ii2i−i0033−33000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.