Finite Group Databasebeta

← Group #13166162

Character table — Group #13166162

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222224444444444668888888888121212121212121212121616161616161616161616161818242436363636363648484848484848484848484872727272108
order1233466333666121212122433336666121244661212121212123366121212121212121288612226666121212121212121212121212242424248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1111111-1-1111111111111-1-1111-111-1-111-1-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-111111-1-111111111111111-1-111-11-1-111-1-111-1-1-1-11111-1-1-1-1-1
χ411111111111111111111111111111-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ51111111−1−i32−1+i3211−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321
χ61111111−1−i32−1+i3211−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1111111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1111-111-1-1−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-1
χ71111111−1−i32−1+i3211−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-111111-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-11-1-1111+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1
χ81111111−1−i32−1+i3211−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321
χ91111111−1+i32−1−i3211−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321
χ101111111−1+i32−1−i3211−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-1111111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1111-111-1-1−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-1
χ111111111−1+i32−1−i3211−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-111111-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-11-1-1111−i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1
χ121111111−1+i32−1−i3211−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321
χ132222-222222222-2-2-2-2-2222222222-2-200-2-22200002222-2-2-2-2-2-2-2-200-2200000000000000000000000
χ142222-222−1−i3−1+i322−1−i3−1+i3-2-2-2-2-22−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31−i300-2-2220000−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i31+i31+i31−i31−i300-2200000000000000000000000
χ152222-222−1+i3−1−i322−1+i3−1−i3-2-2-2-2-22−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i31−i31+i300-2-2220000−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i31−i31−i31+i31+i300-2200000000000000000000000
χ16222-122-122-1-1222-1-1-1222-12-12-12-122022-12-100-1-1-1-1-1-12-12-1-1-1-1-100-1-10200-1-100220000-1-1-1-100000
χ17222-122-122-1-1222-1-1-1222-12-12-12-1220-22-12-10011-1-1-1-12-12-1-1-1-1-100-1-10-2001100-2-20000111100000
χ18222-122-1−1−i3−1+i3-1-1−1−i3−1+i32-1-1-122−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i32−1−i3−1+i3022-12-100-1-11+i321−i321+i321−i32−1−i31+i32−1+i31−i321+i321+i321−i321−i3200-1-10200-1-100−1−i3−1+i300001+i321+i321−i321−i3200000
χ19222-122-1−1−i3−1+i3-1-1−1−i3−1+i32-1-1-122−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i32−1−i3−1+i30-22-12-100111+i321−i321+i321−i32−1−i31+i32−1+i31−i321+i321+i321−i321−i3200-1-10-20011001+i31−i30000−1−i32−1−i32−1+i32−1+i3200000
χ20222-122-1−1+i3−1−i3-1-1−1+i3−1−i32-1-1-122−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i32−1+i3−1−i3022-12-100-1-11−i321+i321−i321+i32−1+i31−i32−1−i31+i321−i321−i321+i321+i3200-1-10200-1-100−1+i3−1−i300001−i321−i321+i321+i3200000
χ21222-122-1−1+i3−1−i3-1-1−1+i3−1−i32-1-1-122−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i32−1+i3−1−i30-22-12-100111−i321+i321−i321+i32−1+i31−i32−1−i31+i321−i321−i321+i321+i3200-1-10-20011001−i31+i30000−1+i32−1+i32−1−i32−1−i3200000
χ22222-1-22-122-1-122-2111-222-12-12-12-1-2-200-212-100−i3i3-1-1-1-1-21-211111001-10000−i3i300000000−i3i3−i3i300000
χ23222-1-22-122-1-122-2111-222-12-12-12-1-2-200-212-100i3−i3-1-1-1-1-21-211111001-10000i3−i300000000i3−i3i3−i300000
χ24222-1-22-1−1−i3−1+i3-1-1−1−i3−1+i3-2111-22−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i321+i31−i300-212-100−i3i31+i321−i321+i321−i321+i3−1−i321−i3−1+i32−1−i32−1−i32−1+i32−1+i32001-10000−i3i300000000−3+i323−i323+i32−3−i3200000
χ25222-1-22-1−1−i3−1+i3-1-1−1−i3−1+i3-2111-22−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i321+i31−i300-212-100i3−i31+i321−i321+i321−i321+i3−1−i321−i3−1+i32−1−i32−1−i32−1+i32−1+i32001-10000i3−i3000000003−i32−3+i32−3−i323+i3200000
χ26222-1-22-1−1+i3−1−i3-1-1−1+i3−1−i3-2111-22−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i321−i31+i300-212-100−i3i31−i321+i321−i321+i321−i3−1+i321+i3−1−i32−1+i32−1+i32−1−i32−1−i32001-10000−i3i3000000003+i32−3−i32−3+i323−i3200000
χ27222-1-22-1−1+i3−1−i3-1-1−1+i3−1−i3-2111-22−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i321−i31+i300-212-100i3−i31−i321+i321−i321+i321−i3−1+i321+i3−1−i32−1+i32−1+i32−1−i32−1−i32001-10000i3−i300000000−3−i323+i323−i32−3+i3200000
χ2822-122-1222-1-122-12-1-122-12-12-12-122220-12-12-1-100-1-1-1-1-12-12-1-1-1-100-1-120-1-1002200-1-1-1-1000000000
χ2922-122-1222-1-122-12-1-122-12-12-12-1222-20-12-121100-1-1-1-1-12-12-1-1-1-100-1-1-201100-2-2001111000000000
χ3022-122-12−1−i3−1+i3-1-1−1−i3−1+i3-12-1-1221+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i3−1−i3−1+i320-12-12-1-1001+i321−i321+i321−i321+i32−1−i31−i32−1+i31+i321+i321−i321−i3200-1-120-1-100−1−i3−1+i3001+i321+i321−i321−i32000000000
χ3122-122-12−1−i3−1+i3-1-1−1−i3−1+i3-12-1-1221+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i3−1−i3−1+i3-20-12-1211001+i321−i321+i321−i321+i32−1−i31−i32−1+i31+i321+i321−i321−i3200-1-1-2011001+i31−i300−1−i32−1−i32−1+i32−1+i32000000000
χ3222-122-12−1+i3−1−i3-1-1−1+i3−1−i3-12-1-1221−i32−1+i31+i32−1−i31−i32−1+i31+i32−1−i3−1+i3−1−i320-12-12-1-1001−i321+i321−i321+i321−i32−1+i31+i32−1−i31−i321−i321+i321+i3200-1-120-1-100−1+i3−1−i3001−i321−i321+i321+i32000000000
χ3322-122-12−1+i3−1−i3-1-1−1+i3−1−i3-12-1-1221−i32−1+i31+i32−1−i31−i32−1+i31+i32−1−i3−1+i3−1−i3-20-12-1211001−i321+i321−i321+i321−i32−1+i31+i32−1−i31−i321−i321+i321+i3200-1-1-2011001−i31+i300−1+i32−1+i32−1−i32−1−i32000000000
χ3422-12-2-1222-1-1221-211-22-12-12-12-12-2-2001-2-12−i3i300-1-1-1-11-21-21111001-100−i3i3000000−i3i3−i3i3000000000
χ3522-12-2-1222-1-1221-211-22-12-12-12-12-2-2001-2-12i3−i300-1-1-1-11-21-21111001-100i3−i3000000i3−i3i3−i3000000000
χ3622-12-2-12−1−i3−1+i3-1-1−1−i3−1+i31-211-221+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i31+i31−i3001-2-12−i3i3001+i321−i321+i321−i32−1−i321+i3−1+i321−i3−1−i32−1−i32−1+i32−1+i32001-100−i3i3000000−3+i323−i323+i32−3−i32000000000
χ3722-12-2-12−1−i3−1+i3-1-1−1−i3−1+i31-211-221+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i31+i31−i3001-2-12i3−i3001+i321−i321+i321−i32−1−i321+i3−1+i321−i3−1−i32−1−i32−1+i32−1+i32001-100i3−i30000003−i32−3+i32−3−i323+i32000000000
χ3822-12-2-12−1+i3−1−i3-1-1−1+i3−1−i31-211-221−i32−1+i31+i32−1−i31−i32−1+i31+i32−1−i31−i31+i3001-2-12−i3i3001−i321+i321−i321+i32−1+i321−i3−1−i321+i3−1+i32−1+i32−1−i32−1−i32001-100−i3i30000003+i32−3−i32−3+i323−i32000000000
χ3922-12-2-12−1+i3−1−i3-1-1−1+i3−1−i31-211-221−i32−1+i31+i32−1−i31−i32−1+i31+i32−1−i31−i31+i3001-2-12i3−i3001−i321+i321−i321+i32−1+i321−i3−1−i321+i3−1+i32−1+i32−1−i32−1−i32001-100i3−i3000000−3−i323+i323−i32−3+i32000000000
χ4033333330033003333-1-1000000000033-1-1-1-1333300000000000033-1-1-1-1-1-1-1-10000000000000000-1
χ4133333330033003333-1-100000000003-3-1-1-1-133-3-3000000000000-3-3-1-1-11-1-11100000000000000001
χ4233333330033003333-1-10000000000-33-1-1-1-1-3-333000000000000-3-3-1-11-111-1-100000000000000001
χ4333333330033003333-1-10000000000-3-3-1-1-1-1-3-3-3-300000000000033-1-11111110000000000000000-1
χ4444-2-24-2-2441144-2-21144-2-2-2-2-2-2-2-24400-2-2-2-200001111-2-2-2-21111001100000000000000000000000
χ4544-2-24-2-2−2−2i3−2+2i311−2−2i3−2+2i3-2-211441+i31+i31−i31−i31+i31+i31−i31−i3−2−2i3−2+2i300-2-2-2-20000−1−i32−1+i32−1−i32−1+i321+i31+i31−i31−i3−1−i32−1−i32−1+i32−1+i32001100000000000000000000000
χ4644-2-24-2-2−2+2i3−2−2i311−2+2i3−2−2i3-2-211441−i31−i31+i31+i31−i31−i31+i31+i3−2+2i3−2−2i300-2-2-2-20000−1+i32−1−i32−1+i32−1−i321−i31−i31+i31+i3−1+i32−1+i32−1−i32−1−i32001100000000000000000000000
χ4744-2-2-4-2-244114422-1-1-44-2-2-2-2-2-2-2-2-4-40022-2-2000011112222-1-1-1-100-1100000000000000000000000
χ4844-2-2-4-2-2−2−2i3−2+2i311−2−2i3−2+2i322-1-1-441+i31+i31−i31−i31+i31+i31−i31−i32+2i32−2i30022-2-20000−1−i32−1+i32−1−i32−1+i32−1−i3−1−i3−1+i3−1+i31+i321+i321−i321−i3200-1100000000000000000000000
χ4944-2-2-4-2-2−2+2i3−2−2i311−2+2i3−2−2i322-1-1-441−i31−i31+i31+i31−i31−i31+i31+i32−2i32+2i30022-2-20000−1+i32−1−i32−1+i32−1−i32−1+i3−1+i3−1−i3−1−i31−i321−i321+i321+i3200-1100000000000000000000000
χ504-4440-4-4-2-24-422000000-2-2-2-22222000000000000-2-2220000000022−22000000000000000000002−22−20
χ514-4440-4-4-2-24-422000000-2-2-2-22222000000000000-2-22200000000−222200000000000000000000−22−220
χ524-4440-4-41+i31−i34-4−1−i3−1+i30000001+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i30000000000001+i31−i3−1−i3−1+i30000000022−2200000000000000000000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ230
χ534-4440-4-41+i31−i34-4−1−i3−1+i30000001+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i30000000000001+i31−i3−1−i3−1+i300000000−222200000000000000000000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ230
χ544-4440-4-41−i31+i34-4−1+i3−1−i30000001−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i30000000000001−i31+i3−1+i3−1−i30000000022−2200000000000000000000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ130
χ554-4440-4-41−i31+i34-4−1+i3−1−i30000001−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i30000000000001−i31+i3−1+i3−1−i300000000−222200000000000000000000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ130
χ566666-666006600-6-6-6-62-200000000000022-2-20000000000000000002-200000000000000000000000
χ57666-366-300-3-3006-3-3-3-2-2000000000006-21-2100-3-300000000000000110-2001100000000000000000
χ58666-366-300-3-3006-3-3-3-2-200000000000-6-21-21003300000000000000110200-1-100000000000000000
χ59666-3-66-300-3-300-63332-20000000000002-1-2100−3i33i300000000000000-110000i3−i300000000000000000
χ60666-3-66-300-3-300-63332-20000000000002-1-21003i3−3i300000000000000-110000−i3i300000000000000000
χ6166-366-3600-3-300-36-3-3-2-20000000000601-21-2-3-3000000000000000011-20110000000000000000000
χ6266-366-3600-3-300-36-3-3-2-20000000000-601-21-23300000000000000001120-1-10000000000000000000
χ6366-36-6-3600-3-3003-6332-2000000000000-121-2−3i33i30000000000000000-1100i3−i30000000000000000000
χ6466-36-6-3600-3-3003-6332-2000000000000-121-23i3−3i30000000000000000-1100−i3i30000000000000000000
χ658-88-40-84-4-4-4444000000-42-424-24-200000000000022-2-200000000000000000000000000000000000
χ668-88-40-842+2i32−2i3-44−2−2i3−2+2i30000002+2i3−1−i32−2i3−1+i3−2−2i31+i3−2+2i31−i3000000000000−1−i3−1+i31+i31−i300000000000000000000000000000000000
χ678-88-40-842−2i32+2i3-44−2+2i3−2−2i30000002−2i3−1+i32+2i3−1−i3−2+2i31−i3−2−2i31+i3000000000000−1+i3−1−i31−i31+i300000000000000000000000000000000000
χ688-8-4804-8-4-4-44440000002-42-4-24-2400000000000022-2-200000000000000000000000000000000000
χ698-8-4804-82+2i32−2i3-44−2−2i3−2+2i3000000−1−i32+2i3−1+i32−2i31+i3−2−2i31−i3−2+2i3000000000000−1−i3−1+i31+i31−i300000000000000000000000000000000000
χ708-8-4804-82−2i32+2i3-44−2+2i3−2−2i3000000−1+i32−2i3−1−i32+2i31−i3−2+2i31+i3−2−2i3000000000000−1+i3−1−i31−i31+i300000000000000000000000000000000000
χ718-8-4-4044-4-42-244006i−6i002222-2-2-2-2000000000000-1-11100003i−3i3i−3i000000000000000000000000000
χ728-8-4-4044-4-42-24400−6i6i002222-2-2-2-2000000000000-1-1110000−3i3i−3i3i000000000000000000000000000
χ738-8-4-40442+2i32−2i32-2−2−2i3−2+2i3006i−6i00−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i30000000000001+i321−i32−1−i32−1+i3200003ζ22−3ζ223ζ14−3ζ14000000000000000000000000000
χ748-8-4-40442+2i32−2i32-2−2−2i3−2+2i300−6i6i00−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i30000000000001+i321−i32−1−i32−1+i320000−3ζ223ζ22−3ζ143ζ14000000000000000000000000000
χ758-8-4-40442−2i32+2i32-2−2+2i3−2−2i3006i−6i00−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i30000000000001−i321+i32−1+i32−1−i3200003ζ14−3ζ143ζ22−3ζ22000000000000000000000000000
χ768-8-4-40442−2i32+2i32-2−2+2i3−2−2i300−6i6i00−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i30000000000001−i321+i32−1+i32−1−i320000−3ζ143ζ14−3ζ223ζ22000000000000000000000000000
χ771212-6-612-6-6003300-6-633-4-40000000000002222000000000000000000-1-100000000000000000000000
χ781212-6-6-12-6-600330066-3-34-4000000000000-2-2220000000000000000001-100000000000000000000000

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