Finite Group Databasebeta

← Group #10693603

Character table — Group #10693603

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212888888881212242424242424242424242424242424248888888844121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91-1-111-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-111-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−iii−i−ii−ii−i11-1-11-1
χ101-1-111-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-111-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiii−iii−i−i−ii−ii-1-111-11
χ111-1-111-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-111-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−ii−i−iiii−ii−i-1-111-11
χ121-1-111-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-111-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−i−iii−ii−ii11-1-11-1
χ131-1-111-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-1-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−i−iii−ii−ii11-1-1-11
χ141-1-111-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-1-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−ii−i−iiii−ii−i-1-1111-1
χ151-1-111-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-1-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−iii−i−i−ii−ii-1-1111-1
χ161-1-111-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-1-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−iii−i−ii−ii−i11-1-1-11
χ172222222222-22-22-2-222222222-2-222-22-2-2-2200000000-2-200000000000000000000000000000022-2-2000000
χ182222222222-22-22-2-222222222-2-222-22-2-2-2200000000-2-2000000000000000000000000000000-2-222000000
χ19222222222-22-22-222-22222222-2-2-2-22-2222-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ20222222222-22-22-222-22222222-2-2-2-22-2222-200000000-2-20000000000000000-2-222-2-2220000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22i−2i2i−2i0000222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ22222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2−2i2i−2i2i000022−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i−2i2i−2i0000-1-1−i−iii−i−iii33−3−333−3−30000000000−i3i3−i3i30000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i−2i2i−2i0000-1-1−i−iii−i−iii−3−333−3−3330000000000i3−i3i3−i30000000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i2i−2i2i0000-1-1ii−i−iii−i−i33−3−333−3−30000000000i3−i3i3−i30000000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i2i−2i2i0000-1-1ii−i−iii−i−i−3−333−3−3330000000000−i3i3−i3i30000000000
χ312222-2-2-2-22020-202-2022-22-2-2-20000202-2-2000002−22−200000000002−22−22−22−2002-2002-200000000002−22−200
χ322222-2-2-2-22020-202-2022-22-2-2-20000202-2-2000002−22−200000000002−22−22−22−200-2200-220000000000−22−2200
χ332222-2-2-2-22020-202-2022-22-2-2-20000202-2-200000−22−220000000000−22−22−22−22002-2002-20000000000−22−2200
χ342222-2-2-2-22020-202-2022-22-2-2-20000202-2-200000−22−220000000000−22−22−22−2200-2200-2200000000002−22−200
χ352-2-222-2-2222-2-2-2-2222-2-2-2222-2-2222-2-222-2-200000000-220000000000000000000000000000002i−2i−2i2i000000
χ362-2-222-2-2222-2-2-2-2222-2-2-2222-2-2222-2-222-2-200000000-22000000000000000000000000000000−2i2i2i−2i000000
χ372-2-222-2-222-22222-2-2-2-2-2-2222-2-22-2-222-2-22200000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ382-2-222-2-222-22222-2-2-2-2-2-2222-2-22-2-222-2-22200000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ392-2-222-2-222-2-22-2222-2-2-2-2222-22-2-2-2-2222-222i−2i−2i2i00002-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ402-2-222-2-222-2-22-2222-2-2-2-2222-22-2-2-2-2222-22−2i2i2i−2i00002-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ412-2-222-2-22-122-22-2-2-22111-1-1-112-2-1-1-1111-1122-2-22i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii000000002i−2i−i−iii0000000000
χ422-2-222-2-22-122-22-2-2-22111-1-1-112-2-1-1-1111-1122-2-2−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i00000000−2i2iii−i−i0000000000
χ432-2-222-2-22-122-22-2-2-22111-1-1-112-2-1-1-1111-11-2-2222i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii00000000−2i2iii−i−i0000000000
χ442-2-222-2-22-122-22-2-2-22111-1-1-112-2-1-1-1111-11-2-222−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i000000002i−2i−i−iii0000000000
χ452-2-222-2-22-1-2-22-2222-2111-1-1-112-2111-1-1-11-12i−2i−2i2i0000-11−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i30000000000−333−30000000000
χ462-2-222-2-22-1-2-22-2222-2111-1-1-112-2111-1-1-11-12i−2i−2i2i0000-11−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300000000003−3−330000000000
χ472-2-222-2-22-1-2-22-2222-2111-1-1-112-2111-1-1-11-1−2i2i2i−2i0000-11ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300000000003−3−330000000000
χ482-2-222-2-22-1-2-22-2222-2111-1-1-112-2111-1-1-11-1−2i2i2i−2i0000-11ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i30000000000−333−30000000000
χ492-2-22-222-22020-20-220-2-222-2-22000020-22-200000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2002i−2i00−2i2i0000000000−222−200
χ502-2-22-222-22020-20-220-2-222-2-22000020-22-200000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i200−2i2i002i−2i00000000002−2−2200
χ512-2-22-222-22020-20-220-2-222-2-22000020-22-200000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2002i−2i00−2i2i00000000002−2−2200
χ522-2-22-222-22020-20-220-2-222-2-22000020-22-200000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i200−2i2i002i−2i0000000000−222−200
χ5344444444-24-44-44-4-44-2-2-2-2-2-2-2-4-4-2-22-2222-200000000220000000000000000000000000000000000000000
χ5444444444-2-44-44-444-4-2-2-2-2-2-2-2-4-422-22-2-2-2200000000220000000000000000000000000000000000000000
χ554444-4-4-4-440-4040-44044-44-4-4-40000-40-444000000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-2040-404-40-2-22-22220000-20-2220000022−2222−220000000000−22−22−22−22000000000000000000000000
χ574444-4-4-4-4-2040-404-40-2-22-22220000-20-22200000−2222−222200000000002−22−22−22−2000000000000000000000000
χ584444-4-4-4-4-20-4040-440-2-22-22220000202-2-200000000000000000006−6−666−6−66000000000000000000000000
χ594444-4-4-4-4-20-4040-440-2-22-22220000202-2-20000000000000000000−666−6−666−6000000000000000000000000
χ6044-4-444-4-4440-40400-44-44-44-4-4004-40-4000400000000000000000000000000000000000000000000000000
χ6144-4-444-4-44-4040-40044-44-44-4-400-4404000-400000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-240-40400-4-22-22-22200-2202000-200000000006−66−66−66−600000000000000000000000000000000
χ6344-4-444-4-4-240-40400-4-22-22-22200-2202000-20000000000−66−66−66−6600000000000000000000000000000000
χ6444-4-444-4-4-2-4040-4004-22-22-222002-20-200020000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ6544-4-444-4-4-2-4040-4004-22-22-222002-20-200020000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ6644-4-4-4-4444000000004-4-4-4-44400000000000000000000000000000000000022−220022−22000000000000000000
χ6744-4-4-4-4444000000004-4-4-4-444000000000000000000000000000000000000−222200−2222000000000000000000
χ684-44-44-44-444040-400-4-44-4-44-44004-404000-400000000000000000000000000000000000000000000000000
χ694-44-44-44-44-40-404004-44-4-44-4400-440-4000400000000000000000000000000000000000000000000000000
χ704-44-44-44-4-24040-400-42-222-22-200-220-2000200000000006−66−6−66−6600000000000000000000000000000000
χ714-44-44-44-4-24040-400-42-222-22-200-220-200020000000000−66−666−66−600000000000000000000000000000000
χ724-44-44-44-4-2-40-4040042-222-22-2002-202000-20000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ734-44-44-44-4-2-40-4040042-222-22-2002-202000-20000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000
χ744-44-4-44-44400000000-444-4-44-4000000000000000000000000000000000000−2i22i2002i2−2i2000000000000000000
χ754-44-4-44-44400000000-444-4-44-40000000000000000000000000000000000002i2−2i200−2i22i2000000000000000000
χ764-4-444-4-44-24-4-4-4-4444222-2-2-22-44-2-222-2-222000000002-20000000000000000000000000000000000000000
χ774-4-444-4-44-2-44444-4-4-4222-2-2-22-4422-2-222-2-2000000002-20000000000000000000000000000000000000000
χ784-4-44-444-440-40404-40-4-444-4-440000-404-44000000000000000000000000000000000000000000000000000
χ794-4-44-444-4-2040-40-44022-2-222-20000-202-2200000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ804-4-44-444-4-2040-40-44022-2-222-20000-202-22000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ814-4-44-444-4-20-40404-4022-2-222-2000020-22-20000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ824-4-44-444-4-20-40404-4022-2-222-2000020-22-20000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ8388-8-8-8-888-400000000-44444-4-4000000000000000000000000000000000000000000000000000000000000
χ848-88-8-88-88-4000000004-4-444-44000000000000000000000000000000000000000000000000000000000000

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