Finite Group Databasebeta

← Group #13150878

Character table — Group #13150878

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12222234466646612121212336666666666121212123666666666121212121212121212121212121222224444222444446666666612121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-11-1-1-11-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-111-11-1-1-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-11-1-1-1-11111111-1-1-1-1-1-111-1-11-1-11
χ61111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-111-11111-1-111-1-1-1-1-1-111-111-1
χ71111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-1-1-111-1-1111111-1-1-111-1
χ81111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11-111-1-1-1-1-1-1111111-1-1111-1-11
χ91111-1-1111111-1-1-111-1-111111-1-1-1-111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-11-1-111-111-1-111-1-111-1-1-1-11111-1-1
χ101111-1-1111111-1-1-111-1-111111-1-1-1-111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-11-11-1-1-1111-1-1-1-11111-1-111-1-1-1-111
χ111111-1-1111111-1-1-111-1-111111-1-1-1-111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-111-111-1-11111-1-1-1-111-1-111-1-111
χ121111-1-1111111-1-1-111-1-111111-1-1-1-111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-111-1-11111-1-111-1-1
χ131111-1-11-1-11111-1-1-1-11111111-1-1-1-1111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-11111-1-1-111-1-11111-1-111-1-1-1-11-11-1
χ141111-1-11-1-11111-1-1-1-11111111-1-1-1-1111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-11-11
χ151111-1-11-1-11111-1-1-1-11111111-1-1-1-1111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-111-1-1-11-11-1-111111111-1-1-1-1-1-1-11-11
χ161111-1-11-1-11111-1-1-1-11111111-1-1-1-1111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-111111-111-1-11-1-1-111-1-1-1-111-1-111111-11-1
χ1722222222222222222222-122-1-1-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12200220020002000-1-1-1-10000-1-1-1-100000000
χ1822222222222222222222-122-1-1-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-200-2-200-2000-200011110000111100000000
χ192222222222222222222-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100220022020000200000-1-1-1-10000-1-1-1-10000
χ202222222222222222222-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100-2-200-2-20-20000-2000001111000011110000
χ212222222-2-2222-222-2-2-2-22-122-1-1-1-1-1-1-12-2-2-2-2-122-1-1-1-1-1-1-11111-2-2111111112200-2-2002000-2000-1-1-1-10000111100000000
χ222222222-2-2222-222-2-2-2-22-122-1-1-1-1-1-1-12-2-2-2-2-122-1-1-1-1-1-1-11111-2-211111111-2-2002200-2000200011110000-1-1-1-100000000
χ232222222-2-2222-222-2-2-2-2-12-1-12222222-11111-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111002200220-20000-200000-1-1110000-1-1110000
χ242222222-2-2222-222-2-2-2-2-12-1-12222222-11111-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111100-2-200-2-202000020000011-1-1000011-1-10000
χ252222-2-2222222-2-2-222-2-22-122-11111-1-122222-1-2-2-1-11111-1-1-111-2-2-1-1-1-1111122002200-2000-2000-1-1110000-1-11100000000
χ262222-2-2222222-2-2-222-2-22-122-11111-1-122222-1-2-2-1-11111-1-1-111-2-2-1-1-1-11111-2-200-2-2002000200011-1-1000011-1-100000000
χ272222-2-2222222-2-2-222-2-2-12-1-12-2-2-2-222-1-1-1-1-1-111-1-11111-122-2-211-1-1-1-11111002200-2-20-20000200000-1-111000011-1-10000
χ282222-2-2222222-2-2-222-2-2-12-1-12-2-2-2-222-1-1-1-1-1-111-1-11111-122-2-211-1-1-1-1111100-2-20022020000-20000011-1-10000-1-1110000
χ292222-2-22-2-22222-2-2-2-2222-122-11111-1-12-2-2-2-2-1-2-2-1-11111-111-1-1221111-1-1-1-12200-2-200-20002000-1-111000011-1-100000000
χ302222-2-22-2-22222-2-2-2-2222-122-11111-1-12-2-2-2-2-1-2-2-1-11111-111-1-1221111-1-1-1-1-2-20022002000-200011-1-10000-1-11100000000
χ312222-2-22-2-22222-2-2-2-222-12-1-12-2-2-2-222-11111-111-1-11111-1-2-222-1-11111-1-1-1-1002200-2-2020000-200000-1-1-1-1000011110000
χ322222-2-22-2-22222-2-2-2-222-12-1-12-2-2-2-222-11111-111-1-11111-1-2-222-1-11111-1-1-1-100-2-200220-2000020000011110000-1-1-1-10000
χ3322-2-20022i−2i2-2-20002i−2i00222-220000-2-2-22i2i−2i−2i2002-20000-22i−2i00002i2i−2i−2i00002-2002i−2i00000000002-20000002i−2i0000000000
χ3422-2-20022i−2i2-2-20002i−2i00222-220000-2-2-22i2i−2i−2i2002-20000-22i−2i00002i2i−2i−2i0000-2200−2i2i0000000000-22000000−2i2i0000000000
χ3522-2-20022i−2i2-2-20002i−2i002-12-2-1−i3−i3i3i311-22i2i−2i−2i-100-11−i3−i3i3i31−ii3−300−i−iii33−3−32-2002i−2i0000000000-11−i3i30000−ii3−300000000
χ3622-2-20022i−2i2-2-20002i−2i002-12-2-1−i3−i3i3i311-22i2i−2i−2i-100-11−i3−i3i3i31−ii3−300−i−iii33−3−3-2200−2i2i00000000001-1i3−i30000i−i−3300000000
χ3722-2-20022i−2i2-2-20002i−2i002-12-2-1i3i3−i3−i311-22i2i−2i−2i-100-11i3i3−i3−i31−ii−3300−i−iii−3−3332-2002i−2i0000000000-11i3−i30000−ii−3300000000
χ3822-2-20022i−2i2-2-20002i−2i002-12-2-1i3i3−i3−i311-22i2i−2i−2i-100-11i3i3−i3−i31−ii−3300−i−iii−3−333-2200−2i2i00000000001-1−i3i30000i−i3−300000000
χ3922-2-2002−2i2i2-2-2000−2i2i00222-220000-2-2-2−2i−2i2i2i2002-20000-2−2i2i0000−2i−2i2i2i00002-200−2i2i00000000002-2000000−2i2i0000000000
χ4022-2-2002−2i2i2-2-2000−2i2i00222-220000-2-2-2−2i−2i2i2i2002-20000-2−2i2i0000−2i−2i2i2i0000-22002i−2i0000000000-220000002i−2i0000000000
χ4122-2-2002−2i2i2-2-2000−2i2i002-12-2-1−i3−i3i3i311-2−2i−2i2i2i-100-11−i3−i3i3i31i−i−3300ii−i−i−3−3332-200−2i2i0000000000-11−i3i30000i−i−3300000000
χ4222-2-2002−2i2i2-2-2000−2i2i002-12-2-1−i3−i3i3i311-2−2i−2i2i2i-100-11−i3−i3i3i31i−i−3300ii−i−i−3−333-22002i−2i00000000001-1i3−i30000−ii3−300000000
χ4322-2-2002−2i2i2-2-2000−2i2i002-12-2-1i3i3−i3−i311-2−2i−2i2i2i-100-11i3i3−i3−i31i−i3−300ii−i−i33−3−32-200−2i2i0000000000-11i3−i30000i−i3−300000000
χ4422-2-2002−2i2i2-2-2000−2i2i002-12-2-1i3i3−i3−i311-2−2i−2i2i2i-100-11i3i3−i3−i31i−i3−300ii−i−i33−3−3-22002i−2i00000000001-1−i3i30000−ii−3300000000
χ452-2-222-2200-2-2202-2000022-2-2-22-22-22-22000022-2-2-22-22-2200000000000000002-2002-20000000000002-20000002-2000000
χ462-2-222-2200-2-2202-2000022-2-2-22-22-22-22000022-2-2-22-22-220000000000000000-2200-22000000000000-22000000-22000000
χ472-2-222-2200-2-2202-20000-1211-22-22-22-2-1−i3i3−i3i3-1-1111-11-11-10000−i3i3−i3i3−i3i3−i3i3−i3i3002-2002-2000000000000-11−i3i30000-11−i3i30000
χ482-2-222-2200-2-2202-20000-1211-22-22-22-2-1−i3i3−i3i3-1-1111-11-11-10000−i3i3−i3i3−i3i3−i3i3−i3i300-2200-220000000000001-1i3−i300001-1i3−i30000
χ492-2-222-2200-2-2202-20000-1211-22-22-22-2-1i3−i3i3−i3-1-1111-11-11-10000i3−i3i3−i3i3−i3i3−i3i3−i3002-2002-2000000000000-11i3−i30000-11i3−i30000
χ502-2-222-2200-2-2202-20000-1211-22-22-22-2-1i3−i3i3−i3-1-1111-11-11-10000i3−i3i3−i3i3−i3i3−i3i3−i300-2200-220000000000001-1−i3i300001-1−i3i30000
χ512-2-22-22200-2-220-22000022-2-2-2-22-222-2200002-22-2-2-22-22200000000000000002-200-220000000000002-2000000-22000000
χ522-2-22-22200-2-220-22000022-2-2-2-22-222-2200002-22-2-2-22-2220000000000000000-22002-2000000000000-220000002-2000000
χ532-2-22-22200-2-220-220000-1211-2-22-222-2-1−i3i3−i3i3-11-1111-11-1-10000i3−i3−i3i3−i3i3i3−i3i3−i3002-200-22000000000000-11i3−i300001-1−i3i30000
χ542-2-22-22200-2-220-220000-1211-2-22-222-2-1−i3i3−i3i3-11-1111-11-1-10000i3−i3−i3i3−i3i3i3−i3i3−i300-22002-20000000000001-1−i3i30000-11i3−i30000
χ552-2-22-22200-2-220-220000-1211-2-22-222-2-1i3−i3i3−i3-11-1111-11-1-10000−i3i3i3−i3i3−i3−i3i3−i3i3002-200-22000000000000-11−i3i300001-1i3−i30000
χ562-2-22-22200-2-220-220000-1211-2-22-222-2-1i3−i3i3−i3-11-1111-11-1-10000−i3i3i3−i3i3−i3−i3i3−i3i300-22002-20000000000001-1i3−i30000-11−i3i30000
χ574444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000000000
χ584444444-4-4444-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-222221-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ594444-4-4444444-4-4-444-4-4-2-2-2-2-22222-2-2-2-2-2-2-212211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000000000
χ604444-4-44-4-44444-4-4-4-444-2-2-2-2-22222-2-2-2222212211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000000000
χ6144-4-40044i−4i4-4-40004i−4i00-24-2240000-4-42−2i−2i2i2i-200-22000024i−4i0000−2i−2i2i2i0000000000000000000000000000000000000000
χ6244-4-40044i−4i4-4-40004i−4i00-2-2-22-2−2i3−2i32i32i3222−2i−2i2i2i1001-1i3i3−i3−i3-1−2i2i23−2300ii−i−i−3−333000000000000000000000000000000000000
χ6344-4-40044i−4i4-4-40004i−4i00-2-2-22-22i32i3−2i3−2i3222−2i−2i2i2i1001-1−i3−i3i3i3-1−2i2i−232300ii−i−i33−3−3000000000000000000000000000000000000
χ6444-4-4004−4i4i4-4-4000−4i4i00-24-2240000-4-422i2i−2i−2i-200-2200002−4i4i00002i2i−2i−2i0000000000000000000000000000000000000000
χ6544-4-4004−4i4i4-4-4000−4i4i00-2-2-22-2−2i3−2i32i32i32222i2i−2i−2i1001-1i3i3−i3−i3-12i−2i−232300−i−iii33−3−3000000000000000000000000000000000000
χ6644-4-4004−4i4i4-4-4000−4i4i00-2-2-22-22i32i3−2i3−2i32222i2i−2i−2i1001-1−i3−i3i3i3-12i−2i23−2300−i−iii−3−333000000000000000000000000000000000000
χ674-44-400400-44-4000000044-44-40000-44-40000400-440000-400000000000000000000000000000000000000000000000000
χ684-44-400400-44-400000004-2-442−2i32i32i3−2i32-2-40000-2002-2−2i32i32i3−2i3200000000000000000000000000000000000000000000000000
χ694-44-400400-44-400000004-2-4422i3−2i3−2i32i32-2-40000-2002-22i3−2i3−2i32i3200000000000000000000000000000000000000000000000000
χ704-44-400400-44-40000000-242-2-40000-44223−23−2323-2002-20000200000023−23−23230000000000000000000000000000000000000000
χ714-44-400400-44-40000000-242-2-40000-442−232323−23-2002-200002000000−232323−230000000000000000000000000000000000000000
χ724-44-400400-44-40000000-2-22-22−2i32i32i3−2i32-2223−23−2323100-11i3−i3−i3i3-1000000−333−3−3i3i3i−3i000000000000000000000000000000000000
χ734-44-400400-44-40000000-2-22-22−2i32i32i3−2i32-22−232323−23100-11i3−i3−i3i3-10000003−3−333i−3i−3i3i000000000000000000000000000000000000
χ744-44-400400-44-40000000-2-22-222i3−2i3−2i32i32-2223−23−2323100-11−i3i3i3−i3-1000000−333−33i−3i−3i3i000000000000000000000000000000000000
χ754-44-400400-44-40000000-2-22-222i3−2i3−2i32i32-22−232323−23100-11−i3i3i3−i3-10000003−3−33−3i3i3i−3i000000000000000000000000000000000000
χ764-4-444-4400-4-4404-400004-2-4-42-22-22-2240000-24-422-22-22-200000000000000000000000000000000000000000000000000
χ774-4-444-4400-4-4404-40000-2-2222-22-22-22-2−2i32i3−2i32i31-22-1-11-11-110000−2i32i3i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ784-4-444-4400-4-4404-40000-2-2222-22-22-22-22i3−2i32i3−2i31-22-1-11-11-1100002i3−2i3−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ794-4-44-44400-4-440-4400004-2-4-422-22-2-2240000-2-44222-22-2-200000000000000000000000000000000000000000000000000
χ804-4-44-44400-4-440-440000-2-22222-22-2-22-2−2i32i3−2i32i312-2-1-1-11-11100002i3−2i3i3−i3i3−i3−i3i3−i3i3000000000000000000000000000000000000
χ814-4-44-44400-4-440-440000-2-22222-22-2-22-22i3−2i32i3−2i312-2-1-1-11-1110000−2i32i3−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000
χ82666666-366-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000002202020000000000000000-1-1-1-1
χ83666666-366-3-3-36-3-3-3-3-3-300000000000000000000000000000000000000000000000000-2-20-20-200000000000000001111
χ84666666-3-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000002-20-2020000000000000000-111-1
χ85666666-3-6-6-3-3-3-6-3-3333300000000000000000000000000000000000000000000000000-22020-200000000000000001-1-11
χ866666-6-6-366-3-3-3-633-3-333000000000000000000000000000000000000000000000000002-2020-20000000000000000-1-111
χ876666-6-6-366-3-3-3-633-3-33300000000000000000000000000000000000000000000000000-220-202000000000000000011-1-1
χ886666-6-6-3-6-6-3-3-363333-3-300000000000000000000000000000000000000000000000000220-20-20000000000000000-11-11
χ896666-6-6-3-6-6-3-3-363333-3-300000000000000000000000000000000000000000000000000-2-2020200000000000000001-11-1
χ901212-12-1200-612i−12i-666000−6i6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-1200-6−12i12i-6660006i−6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-1200-6006-660000063−630000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-1200-6006-6600000−63630000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-121212-12-60066-60-6600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-1212-60066-606-600000000000000000000000000000000000000000000000000000000000000000000000000000000

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