Finite Group Databasebeta

← Group #11775301

Character table — Group #11775301

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222444444444444444666666888888888888812121212121212121216161616161624242424242424242424242424242424242472727272
order122222334466666634666666612121212121222666624666612121212121212244661212121266612121224446688121212121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1111-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111111-1-1-1-1111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111111-1-1
χ91111-1-111-1-111111111-1-1-1111-111-1-1-1-11111111-111-1-11-1-111-1-1-11-1-1-111-1-1111-1-1-11-1i−i11i−i-1-1ii−i−iii−i−ii−ii−i
χ101111-1-111-1-111111111-1-1-1111-111-1-1-1-11111111-111-1-11-1-111-1-1-11-1-1-111-1-1111-1-1-11-1−ii11−ii-1-1−i−iii−i−iii−ii−ii
χ111111-1-111-1-111111111-1-1-1111-111-1-1-1-1111111-11-1-1-1-111111-1-1-11-1-1-111-1-1-1-1-1111-11i−i-1-1−ii11ii−i−i−i−iiii−i−ii
χ121111-1-111-1-111111111-1-1-1111-111-1-1-1-1111111-11-1-1-1-111111-1-1-11-1-1-111-1-1-1-1-1111-11−ii-1-1i−i11−i−iiiii−i−i−iii−i
χ131111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-1-1-1-1-11-111-1-11-1-111-1-11-1111-1-111111-1-1-1-11i−i-1-1i−i11ii−i−iii−i−i−ii−ii
χ141111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-1-1-1-1-11-111-1-11-1-111-1-11-1111-1-111111-1-1-1-11−ii-1-1−ii11−i−iii−i−iiii−ii−i
χ151111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11-1111-1-111-1-1-11111-1i−i11−ii-1-1ii−i−i−i−iii−iii−i
χ161111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11-1111-1-111-1-1-11111-1−ii11i−i-1-1−i−iiiii−i−ii−i−ii
χ1722222222-2-22222222-22222222-2-2-2-2-2-2222222000022-200-2-2-2-22-2-222-2-2-2-20000000000000000000000000000
χ1822222222-2-22222222-22222222-2-2-2-2-2-2-2-2-2-2-2-2000022-200-2-2-2-2-222-2-222220000000000000000000000000000
χ192222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-12222-1-1-1-122-1-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-12-1-12-1-12200-1-100-1-1000000000000
χ202222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-12222-1-1-1-1-2-211-1-1211-1-1-1-1222-1-1-1-1-1-1-211-211-2-200110011000000000000
χ212222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-122-2-2111122-1-1-1-12-1-1-1-1-1-1-2-2-21111112-1-12-1-1-2-200110011000000000000
χ222222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-122-2-21111-2-211-1-1211-1-1-1-1-2-2-2111111-211-2112200-1-100-1-1000000000000
χ232222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-222-1-1-1-100−i3i3-1-1-2−i3i311112-2-2-1-111110−i3i30−i3i30000−i3i300−i3i3000000000000
χ242222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-222-1-1-1-100i3−i3-1-1-2i3−i311112-2-2-1-111110i3−i30i3−i30000i3−i300i3−i3000000000000
χ252222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-2-2-2111100−i3i3-1-1-2−i3i31111-22211-1-1-1-10−i3i30−i3i30000i3−i300i3−i3000000000000
χ262222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-2-2-2111100i3−i3-1-1-2i3−i31111-22211-1-1-1-10i3−i30i3−i30000−i3i300−i3i3000000000000
χ27222222-1222-12-1-122-12-122-1-1-1-12222-1-10000002222-1-1-122-1-1-1-1000000000-1-1-1-1-1-10022002200-1-1-1-1-1-1-1-10000
χ28222222-1222-12-1-122-12-122-1-1-1-12222-1-10000002222-1-1-122-1-1-1-1000000000-1-1-1-1-1-100-2-200-2-200111111110000
χ29222222-1222-12-1-122-12-122-1-1-1-12222-1-1000000-2-2-2-2-1-1-1-2-2-1-1-1-1000000000111111002200-2-200-1-1-1-111110000
χ30222222-1222-12-1-122-12-122-1-1-1-12222-1-1000000-2-2-2-2-1-1-1-2-2-1-1-1-100000000011111100-2-20022001111-1-1-1-10000
χ312222-2-222222222222-2-2-2-2222-2-2-222222222220000-2-2-200-2-222-2-22-2-2-2-2220000000000000000000000000000
χ322222-2-222222222222-2-2-2-2222-2-2-22222-2-2-2-2-2-20000-2-2-200-2-22222-22222-2-20000000000000000000000000000
χ332222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-12222-1-1-1-100−i3i311-2i3−i311-1-1-2-221111-1-10−i3i30i3−i30000−i3i300i3−i3000000000000
χ342222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-12222-1-1-1-100i3−i311-2−i3i311-1-1-2-221111-1-10i3−i30−i3i30000i3−i300−i3i3000000000000
χ352222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-122-2-2111100−i3i311-2i3−i311-1-122-2-1-1-1-1110−i3i30i3−i30000i3−i300−i3i3000000000000
χ362222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-122-2-2111100i3−i311-2−i3i311-1-122-2-1-1-1-1110i3−i30−i3i30000−i3i300i3−i3000000000000
χ372222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-222-1-1-1-12-2-1-111211-1-111-22-211-1-1112-1-1-2112-200-1-10011000000000000
χ382222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-222-1-1-1-1-2211112-1-1-1-111-22-211-1-111-2112-1-1-22001100-1-1000000000000
χ392222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-2-2-211112-2-1-111211-1-1112-22-1-111-1-12-1-1-211-22001100-1-1000000000000
χ402222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-2-2-21111-2211112-1-1-1-1112-22-1-111-1-1-2112-1-12-200-1-10011000000000000
χ412222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-2110000002-22211-1-2-2-1-111000000000-1-1-1111002i−2i002i−2i00−i−iii−i−iii0000
χ422222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-2110000002-22211-1-2-2-1-111000000000-1-1-111100−2i2i00−2i2i00ii−i−iii−i−i0000
χ432222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-211000000-22-2-211-122-1-111000000000111-1-1-1002i−2i00−2i2i00−i−iiiii−i−i0000
χ442222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-211000000-22-2-211-122-1-111000000000111-1-1-100−2i2i002i−2i00ii−i−i−i−iii0000
χ45444444-24-4-4-24-2-244-2-4-244-2-2-2-2-4-4-4-4220000000000-2-220022220000000000000000000000000000000000000
χ46444444-2-244-2-2-2-2-2-214-2-2-2111-2-2-2-2-2-2-200000044-2-211-2-2-21111000000000-211-2110000000000000000000000
χ47444444-2-244-2-2-2-2-2-214-2-2-2111-2-2-2-2-2-2-2000000-4-42211-22211110000000002-1-12-1-10000000000000000000000
χ48444444-2-2-4-4-2-2-2-2-2-21-4-2-2-2111-222222200000000−2i32i3112−2i32i3-1-1-1-10000000000i3−i30i3−i30000000000000000000000
χ49444444-2-2-4-4-2-2-2-2-2-21-4-2-2-2111-2222222000000002i3−2i31122i3−2i3-1-1-1-10000000000−i3i30−i3i30000000000000000000000
χ504444-4-4-2444-24-2-244-2-42-4-4-2-2-22-4-444-2-200000000002220022-2-20000000000000000000000000000000000000
χ514444-4-4-2-244-2-2-2-2-2-21-4222111222-2-2-2-200000000−2i32i3-1-122i3−2i3-1-1110000000000i3−i30−i3i30000000000000000000000
χ524444-4-4-2-244-2-2-2-2-2-21-4222111222-2-2-2-2000000002i3−2i3-1-12−2i32i3-1-1110000000000−i3i30i3−i30000000000000000000000
χ534444-4-4-2-2-4-4-2-2-2-2-2-2142221112-2-222220000004-4-2-2-1-1-22211-1-1000000000-2112-1-10000000000000000000000
χ544444-4-4-2-2-4-4-2-2-2-2-2-2142221112-2-22222000000-4422-1-1-2-2-211-1-10000000002-1-1-2110000000000000000000000
χ5544-4-400444i−4i44-4-4-4-4400004-4-40004i−4i4i−4i000000000000000004i−4i0000000000000000000000000000000000000
χ5644-4-40044−4i4i44-4-4-4-4400004-4-4000−4i4i−4i4i00000000000000000−4i4i0000000000000000000000000000000000000
χ5744-4-4004-24i−4i4-2-4-422-20000-222000−2i2i4i−4i00−2i3−2i32i32i300000000000−2i2i000000023−230000000000000000000000000000
χ5844-4-4004-24i−4i4-2-4-422-20000-222000−2i2i4i−4i002i32i3−2i3−2i300000000000−2i2i0000000−23230000000000000000000000000000
χ5944-4-4004-2−4i4i4-2-4-422-20000-2220002i−2i−4i4i00−2i3−2i32i32i3000000000002i−2i0000000−23230000000000000000000000000000
χ6044-4-4004-2−4i4i4-2-4-422-20000-2220002i−2i−4i4i002i32i3−2i3−2i3000000000002i−2i000000023−230000000000000000000000000000
χ6144-4-400-244i−4i-2422-4-4-20000-2220004i−4i−2i2i00000000000000000−2i2i0000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000
χ6244-4-400-244i−4i-2422-4-4-20000-2220004i−4i−2i2i00000000000000000−2i2i0000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000
χ6344-4-400-24−4i4i-2422-4-4-20000-222000−4i4i2i−2i000000000000000002i−2i0000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000
χ6444-4-400-24−4i4i-2422-4-4-20000-222000−4i4i2i−2i000000000000000002i−2i0000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000
χ654-44-4004400-4-44-44-440000-44-400000004-44-44-400000000000000000000000000000000000000000000000000
χ664-44-4004400-4-44-44-440000-44-40000000-44-44-4400000000000000000000000000000000000000000000000000
χ674-44-4004-200-424-4-22-200002-220−2i32i300004-4-22-22000000000−2i32i30000000−2i32i3000000000000000000000000000000
χ684-44-4004-200-424-4-22-200002-220−2i32i30000-442-22-2000000000−2i32i300000002i3−2i3000000000000000000000000000000
χ694-44-4004-200-424-4-22-200002-2202i3−2i300004-4-22-220000000002i3−2i300000002i3−2i3000000000000000000000000000000
χ704-44-4004-200-424-4-22-200002-2202i3−2i30000-442-22-20000000002i3−2i30000000−2i32i3000000000000000000000000000000
χ714-4-444-44400-4-4-44-4440-44-4-4-44400000000000000004-400000000000000000000000000000000000000000000
χ724-4-444-44-200-42-442-2-20-4-2222-2400000000−2i32i32i3−2i30000-220000000000−2i32i300000000000000000000000000000000
χ734-4-444-44-200-42-442-2-20-4-2222-24000000002i3−2i3−2i32i30000-2200000000002i3−2i300000000000000000000000000000000
χ744-4-444-4-24002-42-2-44-2024-422-2-20000000000000000-22000000000000000000000000000000000000i6−i6i6−i60000
χ754-4-444-4-24002-42-2-44-2024-422-2-20000000000000000-22000000000000000000000000000000000000−i6i6−i6i60000
χ764-4-44-444400-4-4-44-44404-44-4-44-40000000000000000-4400000000000000000000000000000000000000000000
χ774-4-44-444-200-42-442-2-2042-222-2-400000000−2i32i32i3−2i300002-200000000002i3−2i300000000000000000000000000000000
χ784-4-44-444-200-42-442-2-2042-222-2-4000000002i3−2i3−2i32i300002-20000000000−2i32i300000000000000000000000000000000
χ794-4-44-44-24002-42-2-44-20-2-4422-2200000000000000002-20000000000000000000000000000000000006−6−660000
χ804-4-44-44-24002-42-2-44-20-2-4422-2200000000000000002-2000000000000000000000000000000000000−666−60000
χ8188-8-800-4-48i−8i-4-44444200002-2-2000−4i4i−4i4i000000000000000002i−2i0000000000000000000000000000000000000
χ8288-8-800-4-4−8i8i-4-44444200002-2-20004i−4i4i−4i00000000000000000−2i2i0000000000000000000000000000000000000
χ838-88-800-48004-8-448-8-400004-44000000000000000000000000000000000000000000000000000000000000000
χ848-88-800-4-40044-44-4420000-22-20−4i34i300000000000000000002i3−2i3000000000000000000000000000000000000000
χ858-88-800-4-40044-44-4420000-22-204i3−4i30000000000000000000−2i32i3000000000000000000000000000000000000000
χ868-8-888-8-4-400444-44-4204-44-2-22-400000000000000002-200000000000000000000000000000000000000000000
χ878-8-88-88-4-400444-44-420-44-4-2-2240000000000000000-2200000000000000000000000000000000000000000000

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