Finite Group Databasebeta

← Group #11771842

Character table — Group #11771842

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222244444444444444444444444488888888888888888888824242424242424242424242424242424242424242424242472727272
order12222233666666344446666666666612121212121212124121212121212121212121212121212121212121288888888242424242424242424242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1
χ6111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111
χ7111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ8111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ92222222222222222-2-222222222222222-2-2-2-222-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222222222222-222-222222222222-2-22222-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ112222222-12-12-12-1-1222222-1-1-1-1-1-1-1-1-122-1-1-1-1222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ122222222-12-12-12-1-1222222-1-1-1-1-1-1-1-1-122-1-1-1-1222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ132222222-12-12-12-1-12-2-2222-1-1-1-1-1-1-1-1-122111122-2-1-1-2-211-2-2-1-1-1-1111111110000000033−3−333−3−3000000000000
χ142222222-12-12-12-1-12-2-2222-1-1-1-1-1-1-1-1-122111122-2-1-1-2-211-2-2-1-1-1-11111111100000000−3−333−3−333000000000000
χ152222222-12-12-12-1-1-222-222-1-1-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-211-2-2112211111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ162222222-12-12-12-1-1-222-222-1-1-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-211-2-2112211111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ172222222-12-12-12-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-2-21111-2-221122-1-1-2-21111-1-1-1-111112i2i−2i−2i0000−i−i−i−iiiii000000000000
χ182222222-12-12-12-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-2-21111-2-221122-1-1-2-21111-1-1-1-11111−2i−2i2i2i0000iiii−i−i−i−i000000000000
χ19222222-12-12-12-12-12222-1-122-1-1-1-1-1-1-1-1-12222-1-1222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ20222222-12-12-12-12-12222-1-122-1-1-1-1-1-1-1-1-12222-1-1222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ21222222-12-12-12-12-12-2-22-1-122-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-22211-2-211-1-1-1-1111111110000000000000000−i3−i3i3i3−i3−i3i3i30000
χ22222222-12-12-12-12-12-2-22-1-122-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-22211-2-211-1-1-1-1111111110000000000000000i3i3−i3−i3i3i3−i3−i30000
χ23222222-12-12-12-12-1-222-2-1-122-1-1-1-1-1-1-111222211-2-2-211-2-2-1-111111111-1-1-1-1000000000000000033−3−3−3−3330000
χ24222222-12-12-12-12-1-222-2-1-122-1-1-1-1-1-1-111222211-2-2-211-2-2-1-111111111-1-1-1-10000000000000000−3−33333−3−30000
χ25222222-12-12-12-12-1-2-2-2-2-1-122-1-1-1-1-1-1-111-2-2-2-2112-2-2-1-122111111-1-1-1-1111100002i2i−2i−2i00000000−i−i−i−iiiii0000
χ26222222-12-12-12-12-1-2-2-2-2-1-122-1-1-1-1-1-1-111-2-2-2-2112-2-2-1-122111111-1-1-1-111110000−2i−2i2i2i00000000iiii−i−i−i−i0000
χ272-2-222-222-2-222-2-2202i−2i02-22-222-2-2-22-2002i2i−2i−2i0000000002i−2i000000002i2i−2i−2i00001+i−1−i1−i−1+i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ282-2-222-222-2-222-2-2202i−2i02-22-222-2-2-22-2002i2i−2i−2i0000000002i−2i000000002i2i−2i−2i0000−1−i1+i−1+i1−i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ292-2-222-222-2-222-2-220−2i2i02-22-222-2-2-22-200−2i−2i2i2i000000000−2i2i00000000−2i−2i2i2i00001−i−1+i1+i−1−i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ302-2-222-222-2-222-2-220−2i2i02-22-222-2-2-22-200−2i−2i2i2i000000000−2i2i00000000−2i−2i2i2i0000−1+i1−i−1−i1+i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ312-2-222-2-121-2-121-2-102i−2i0-112-2-1-1111-11−i3i32i2i−2i−2i−i3i30003−300−ii−i3−i3i3i333−3−3−i−iii00001+i−1−i1−i−1+i00000000−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ220000
χ322-2-222-2-121-2-121-2-102i−2i0-112-2-1-1111-11−i3i32i2i−2i−2i−i3i30003−300−ii−i3−i3i3i333−3−3−i−iii0000−1−i1+i−1+i1−i00000000ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ220000
χ332-2-222-2-121-2-121-2-102i−2i0-112-2-1-1111-11i3−i32i2i−2i−2ii3−i3000−3300−iii3i3−i3−i3−3−333−i−iii00001+i−1−i1−i−1+i00000000−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ140000
χ342-2-222-2-121-2-121-2-102i−2i0-112-2-1-1111-11i3−i32i2i−2i−2ii3−i3000−3300−iii3i3−i3−i3−3−333−i−iii0000−1−i1+i−1+i1−i00000000ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ140000
χ352-2-222-2-121-2-121-2-10−2i2i0-112-2-1-1111-11−i3i3−2i−2i2i2i−i3i3000−3300i−i−i3−i3i3i3−3−333ii−i−i00001−i−1+i1+i−1−i00000000−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ220000
χ362-2-222-2-121-2-121-2-10−2i2i0-112-2-1-1111-11−i3i3−2i−2i2i2i−i3i3000−3300i−i−i3−i3i3i3−3−333ii−i−i0000−1+i1−i−1−i1+i00000000ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ220000
χ372-2-222-2-121-2-121-2-10−2i2i0-112-2-1-1111-11i3−i3−2i−2i2i2ii3−i30003−300i−ii3i3−i3−i333−3−3ii−i−i00001−i−1+i1+i−1−i00000000−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ140000
χ382-2-222-2-121-2-121-2-10−2i2i0-112-2-1-1111-11i3−i3−2i−2i2i2ii3−i30003−300i−ii3i3−i3−i333−3−3ii−i−i0000−1+i1−i−1−i1+i00000000ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ140000
χ392-2-22-2222-2-222-2-22200-2-22-22-2-222-22-2220000-2-202-20000002-22-200000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000000000000
χ402-2-22-2222-2-222-2-22200-2-22-22-2-222-22-2220000-2-202-20000002-22-200000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000000000000
χ412-2-22-2222-2-222-2-22-2002-22-22-2-222-22-2-2-20000220-22000000-22-22000000002−2−2200002−22−2−22−22000000000000
χ422-2-22-2222-2-222-2-22-2002-22-22-2-222-22-2-2-20000220-22000000-22-2200000000−222−20000−22−222−22−2000000000000
χ432-2-22-222-1-212-1-21-1200-2-221-111-1-11-11223−33−3-2-20-11003−300-11-113−33−33−33−3−i2i2−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ442-2-22-222-1-212-1-21-1200-2-221-111-1-11-11223−33−3-2-20-11003−300-11-113−33−33−33−3i2−i2i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ452-2-22-222-1-212-1-21-1200-2-221-111-1-11-1122−33−33-2-20-1100−3300-11-11−33−33−33−33−i2i2−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ462-2-22-222-1-212-1-21-1200-2-221-111-1-11-1122−33−33-2-20-1100−3300-11-11−33−33−33−33i2−i2i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ472-2-22-222-1-212-1-21-1-2002-221-111-1-11-11-2-23−33−32201-100−33001-11-1−33−333−33−32−2−220000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ482-2-22-222-1-212-1-21-1-2002-221-111-1-11-11-2-23−33−32201-100−33001-11-1−33−333−33−3−222−20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ492-2-22-222-1-212-1-21-1-2002-221-111-1-11-11-2-2−33−332201-1003−3001-11-13−33−3−33−332−2−220000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ502-2-22-222-1-212-1-21-1-2002-221-111-1-11-11-2-2−33−332201-1003−3001-11-13−33−3−33−33−222−20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ51444444-2-2-2-2-2-2-2-214444-2-2-2-21111111-2-2-2-2-2-2-2-24-2-2-2-2-2-2-2-21111111111110000000000000000000000000000
χ52444444-2-2-2-2-2-2-2-214-4-44-2-2-2-21111111-2-22222-2-2-4-2-22222221111-1-1-1-1-1-1-1-10000000000000000000000000000
χ53444444-2-2-2-2-2-2-2-21-444-4-2-2-2-2111111122-2-2-2-222-4222222-2-2-1-1-1-1-1-1-1-111110000000000000000000000000000
χ54444444-2-2-2-2-2-2-2-21-4-4-4-4-2-2-2-2111111122222222422-2-2-2-222-1-1-1-11111-1-1-1-10000000000000000000000000000
χ554444-4-44444444440000-4-4-4-4-4-4-4-4444000000000000000000000000000000000000000000000000000000000
χ564444-4-44-24-24-24-2-20000-4-4222222-2-2-200−2i32i32i3−2i30000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ574444-4-44-24-24-24-2-20000-4-4222222-2-2-2002i3−2i3−2i32i300000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ584444-4-4-24-24-24-24-2000022-4-42222-2-2-2−2i32i300002i3−2i3000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ594444-4-4-24-24-24-24-2000022-4-42222-2-2-22i3−2i30000−2i32i30000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ604444-4-4-2-2-2-2-2-2-2-2100002222-1-1-1-1111−2i32i3−2i32i32i3−2i32i3−2i3000000000i3−i3−i3i3-333-3i3−i3−i3i30000000000000000000000000000
χ614444-4-4-2-2-2-2-2-2-2-2100002222-1-1-1-1111−2i32i32i3−2i3−2i32i32i3−2i3000000000i3−i3−i3i33-3-33−i3i3i3−i30000000000000000000000000000
χ624444-4-4-2-2-2-2-2-2-2-2100002222-1-1-1-11112i3−2i3−2i32i32i3−2i3−2i32i3000000000−i3i3i3−i33-3-33i3−i3−i3i30000000000000000000000000000
χ634444-4-4-2-2-2-2-2-2-2-2100002222-1-1-1-11112i3−2i32i3−2i3−2i32i3−2i32i3000000000−i3i3i3−i3-333-3−i3i3i3−i30000000000000000000000000000
χ6444-4-4004444-4-4-4-440000000000004-4-400000000000000000000000000000000000000000000000000000002-2
χ6544-4-4004444-4-4-4-440000000000004-4-40000000000000000000000000000000000000000000000000000000-22
χ664-44-40044-4-4-4-4444000000000000-4-44000000000000000000000000000000000000000000000000000002i−2i00
χ674-44-40044-4-4-4-4444000000000000-4-4400000000000000000000000000000000000000000000000000000−2i2i00
χ684-4-444-44-2-424-2-42-204i−4i04-4-22-2-2222-2200−2i−2i2i2i0000000004i−4i00000000−2i−2i2i2i0000000000000000000000000000
χ694-4-444-44-2-424-2-42-20−4i4i04-4-22-2-2222-22002i2i−2i−2i000000000−4i4i000000002i2i−2i−2i0000000000000000000000000000
χ704-4-444-4-2-222-2-222104i−4i0-22-2211-1-1-11-1−2i32i3−2i−2i2i2i−2i32i300023−2300−2i2ii3i3−i3−i3−3−333ii−i−i0000000000000000000000000000
χ714-4-444-4-2-222-2-222104i−4i0-22-2211-1-1-11-12i3−2i3−2i−2i2i2i2i3−2i3000−232300−2i2i−i3−i3i3i333−3−3ii−i−i0000000000000000000000000000
χ724-4-444-4-2-222-2-22210−4i4i0-22-2211-1-1-11-1−2i32i32i2i−2i−2i−2i32i3000−2323002i−2ii3i3−i3−i333−3−3−i−iii0000000000000000000000000000
χ734-4-444-4-2-222-2-22210−4i4i0-22-2211-1-1-11-12i3−2i32i2i−2i−2i2i3−2i300023−23002i−2i−i3−i3i3i3−3−333−i−iii0000000000000000000000000000
χ744-4-44-44-242-4-242-4-2400-42-2-4422-2-22-22-2-200002204-4000000-22-22000000000000000000000000000000000000
χ754-4-44-44-242-4-242-4-2-40042-2-4422-2-22-22220000-2-20-440000002-22-2000000000000000000000000000000000000
χ764-4-44-44-2-222-2-2221400-42-22-2-1-111-11-1-2-223−2323−23220-220023−23001-11-1−33−33−33−330000000000000000000000000000
χ774-4-44-44-2-222-2-2221400-42-22-2-1-111-11-1-2-2−2323−2323220-2200−2323001-11-13−33−33−33−30000000000000000000000000000
χ784-4-44-44-2-222-2-2221-40042-22-2-1-111-11-12223−2323−23-2-202-200−232300-11-113−33−3−33−330000000000000000000000000000
χ794-4-44-44-2-222-2-2221-40042-22-2-1-111-11-122−2323−2323-2-202-20023−2300-11-11−33−333−33−30000000000000000000000000000
χ8088-8-8008-48-4-84-84-4000000000000-444000000000000000000000000000000000000000000000000000000000
χ8188-8-800-48-484-84-8-4000000000000-444000000000000000000000000000000000000000000000000000000000
χ8288-8-800-4-4-4-444442000000006-66-62-2-2000000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4-4-44444200000000-66-662-2-2000000000000000000000000000000000000000000000000000000000
χ848-88-8008-4-84-848-4-400000000000044-4000000000000000000000000000000000000000000000000000000000
χ858-88-800-484-84-8-48-400000000000044-4000000000000000000000000000000000000000000000000000000000
χ868-88-800-4-44444-4-42000000006-6-66-2-22000000000000000000000000000000000000000000000000000000000
χ878-88-800-4-44444-4-4200000000-666-6-2-22000000000000000000000000000000000000000000000000000000000

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