Finite Group Databasebeta

← Group #10693873

Character table — Group #10693873

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
χ91-1111-1-1-11-1-1-11-1111-1-1-1111-11-1111-1-1-11-1ii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1i−iii−i−iii−i−i11-1-1i−i
χ101-1111-1-1-11-1-1-11-1111-1-1-1111-11-1111-1-1-11-1ii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111i−iii−i−i−i−iii-1-111−ii
χ111-1111-1-1-11-1-1-11-1111-1-1-1111-11-1111-1-1-11-1ii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-111111111-1-1-1-1−ii−i−iiiii−i−i-1-111−ii
χ121-1111-1-1-11-1-1-11-1111-1-1-1111-11-1111-1-1-11-1ii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111-1-1-1-11111−ii−i−iii−i−iii11-1-1i−i
χ131-1111-1-1-11-1-1-11-1111-1-1-1111-11-1111-1-1-11-1−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−ii−i−iii−i−iii11-1-1−ii
χ141-1111-1-1-11-1-1-11-1111-1-1-1111-11-1111-1-1-11-1−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−ii−i−iiiii−i−i-1-111i−i
χ151-1111-1-1-11-1-1-11-1111-1-1-1111-11-1111-1-1-11-1−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-111111111-1-1-1-1i−iii−i−i−i−iii-1-111i−i
χ161-1111-1-1-11-1-1-11-1111-1-1-1111-11-1111-1-1-11-1−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-11111-1-1-1-11111i−iii−i−iii−i−i11-1-1−ii
χ1722222222222-22-2-2-222222222-2-22-2-222-22-200000000-2-20000000000000000000000000000002-22-2000000
χ1822222222222-22-2-2-222222222-2-22-2-222-22-200000000-2-2000000000000000000000000000000-22-22000000
χ19222222222-2-22-2222-22222222-2-2-222-2-22-2200000000-2-2000000000000000022-2-222-2-20000000000000000
χ20222222222-2-22-2222-22222222-2-2-222-2-22-2200000000-2-20000000000000000-2-222-2-2220000000000000000
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
χ31222-2-2-2-2220020-22-202-2-22-2-220002-20020-20000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2002-2002-20000000000−i2i2−i2i200
χ32222-2-2-2-2220020-22-202-2-22-2-220002-20020-20000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i200-2200-220000000000i2−i2i2−i200
χ33222-2-2-2-2220020-22-202-2-22-2-220002-20020-20000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2002-2002-20000000000i2−i2i2−i200
χ34222-2-2-2-2220020-22-202-2-22-2-220002-20020-20000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i200-2200-220000000000−i2i2−i2i200
χ352-2222-2-2-22222-22-2-2-2-2-2-2222-22-2-2-2-2222-222-2-2200002-222-2-2-2-22200000000000000000000000000000000
χ362-2222-2-2-22222-22-2-2-2-2-2-2222-22-2-2-2-2222-22-222-200002-2-2-22222-2-200000000000000000000000000000000
χ372-2222-2-2-2222-2-2-222-2-2-2-2222-2-22-22222-2-2-200000000-22000000000000000022-2-2-2-2220000000000000000
χ382-2222-2-2-2222-2-2-222-2-2-2-2222-2-22-22222-2-2-200000000-220000000000000000-2-22222-2-20000000000000000
χ392-2222-2-2-22-2-2222-2-22-2-2-2222-2-222-2-2-2-222200000000-220000000000000000000000000000002i−2i−2i2i000000
χ402-2222-2-2-22-2-2222-2-22-2-2-2222-2-222-2-2-2-222200000000-22000000000000000000000000000000−2i2i2i−2i000000
χ412-2222-2-2-2-1222-22-2-2-2111-1-1-112-2111-1-1-11-12-2-220000-11-1-11111-1-133−3−3−3−3330000000000−333−30000000000
χ422-2222-2-2-2-1222-22-2-2-2111-1-1-112-2111-1-1-11-12-2-220000-11-1-11111-1-1−3−33333−3−300000000003−3−330000000000
χ432-2222-2-2-2-1222-22-2-2-2111-1-1-112-2111-1-1-11-1-222-20000-1111-1-1-1-11133−3−3−3−33300000000003−3−330000000000
χ442-2222-2-2-2-1222-22-2-2-2111-1-1-112-2111-1-1-11-1-222-20000-1111-1-1-1-111−3−33333−3−30000000000−333−30000000000
χ452-2222-2-2-2-1-2-2-22-2222111-1-1-112-2-1-1-1111-112i2i−2i−2i22-2-2-11−i−i−i−iiiii-1-1-1-11111000000002i−2i−i−iii0000000000
χ462-2222-2-2-2-1-2-2-22-2222111-1-1-112-2-1-1-1111-112i2i−2i−2i-2-222-11−i−i−i−iiiii1111-1-1-1-100000000−2i2iii−i−i0000000000
χ472-2222-2-2-2-1-2-2-22-2222111-1-1-112-2-1-1-1111-11−2i−2i2i2i22-2-2-11iiii−i−i−i−i-1-1-1-1111100000000−2i2iii−i−i0000000000
χ482-2222-2-2-2-1-2-2-22-2222111-1-1-112-2-1-1-1111-11−2i−2i2i2i-2-222-11iiii−i−i−i−i1111-1-1-1-1000000002i−2i−i−iii0000000000
χ492-22-2-222-2200-2022-20-2222-2-2-20002-200-2020000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2002-200-220000000000−i2i2i2−i200
χ502-22-2-222-2200-2022-20-2222-2-2-20002-200-2020000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i200-22002-20000000000i2−i2−i2i200
χ512-22-2-222-2200-2022-20-2222-2-2-20002-200-2020000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2002-200-220000000000i2−i2−i2i200
χ522-22-2-222-2200-2022-20-2222-2-2-20002-200-2020000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i200-22002-20000000000−i2i2i2−i200
χ5344444444-244-44-4-4-44-2-2-2-2-2-2-2-4-4-222-2-22-2200000000220000000000000000000000000000000000000000
χ5444444444-2-4-44-4444-4-2-2-2-2-2-2-2-4-42-2-222-22-200000000220000000000000000000000000000000000000000
χ55444-4-4-4-44400-404-4404-4-44-4-44000-4400-40400000000000000000000000000000000000000000000000000
χ56444-4-4-4-44-20040-44-40-222-222-2000-2200-2020000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ57444-4-4-4-44-20040-44-40-222-222-2000-2200-20200002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ58444-4-4-4-44-200-404-440-222-222-20002-20020-2000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ59444-4-4-4-44-200-404-440-222-222-20002-20020-2000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ6044-44-44-4-440000000044-4-44-4-400000000000000000000000000000000000022−220022−22000000000000000000
χ6144-44-44-4-440000000044-4-44-4-4000000000000000000000000000000000000−222200−2222000000000000000000
χ6244-4-44-44-444-404000-44-44-4-44-400-4004-404000000000000000000000000000000000000000000000000000
χ6344-4-44-44-44-440-400044-44-4-44-400400-440-4000000000000000000000000000000000000000000000000000
χ6444-4-44-44-4-24-404000-4-22-222-2200200-220-2000000000006−66−66−66−600000000000000000000000000000000
χ6544-4-44-44-4-24-404000-4-22-222-2200200-220-200000000000−66−66−66−6600000000000000000000000000000000
χ6644-4-44-44-4-2-440-40004-22-222-2200-2002-20200000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ6744-4-44-44-4-2-440-40004-22-222-2200-2002-20200000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ684-4444-4-4-4-244-4-4-444-4222-2-2-22-442-2-2-2-2222000000002-20000000000000000000000000000000000000000
χ694-4444-4-4-4-2-4-4444-4-44222-2-2-22-44-22222-2-2-2000000002-20000000000000000000000000000000000000000
χ704-44-4-444-440040-4-440-4444-4-4-4000-440040-400000000000000000000000000000000000000000000000000
χ714-44-4-444-4-20040-4-4402-2-2-22220002-200-202000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ724-44-4-444-4-20040-4-4402-2-2-22220002-200-202000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ734-44-4-444-4-200-4044-402-2-2-2222000-220020-20000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ744-44-4-444-4-200-4044-402-2-2-2222000-220020-200002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ754-4-44-4-444400000000-4-44-44-4400000000000000000000000000000000000022−2200−2222000000000000000000
χ764-4-44-4-444400000000-4-44-44-44000000000000000000000000000000000000−22220022−22000000000000000000
χ774-4-4-444-4444-40-40004-44-4-4-444004004-40-4000000000000000000000000000000000000000000000000000
χ784-4-4-444-444-4404000-4-44-4-4-44400-400-4404000000000000000000000000000000000000000000000000000
χ794-4-4-444-44-24-40-400042-2222-2-200-200-2202000000000006−6−66−666−600000000000000000000000000000000
χ804-4-4-444-44-24-40-400042-2222-2-200-200-220200000000000−666−66−6−6600000000000000000000000000000000
χ814-4-4-444-44-2-4404000-42-2222-2-2002002-20-200000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ824-4-4-444-44-2-4404000-42-2222-2-2002002-20-200000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ8388-88-88-8-8-400000000-4-444-444000000000000000000000000000000000000000000000000000000000000
χ848-8-88-8-888-40000000044-44-44-4000000000000000000000000000000000000000000000000000000000000

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