Finite Group Databasebeta

← Group #10693582

Character table — Group #10693582

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
χ91-111-1-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-111-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−iii−i−iii−i−i11-1-11-1
χ101-111-1-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-111-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiii−iii−i−i−i−iii-1-111-11
χ111-111-1-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-111-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−ii−i−iiiii−i−i-1-111-11
χ121-111-1-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-111-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−i−iii−i−iii11-1-11-1
χ131-111-1-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-1-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−i−iii−i−iii11-1-1-11
χ141-111-1-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-1-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−ii−i−iiiii−i−i-1-1111-1
χ151-111-1-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-1-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−iii−i−i−i−iii-1-1111-1
χ161-111-1-1-11111-11-1-1-11-1-1-1111-11-1111-1-1-11-1-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−iii−i−iii−i−i11-1-1-11
χ172222222222-2-22-222-22222222-2-22-2-222-22-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ182222222222-2-22-222-22222222-2-22-2-222-22-200000000-2-20000000000000000-2-222-2-2220000000000000000
χ19222222222-222-22-2-222222222-2-2-222-2-22-2200000000-2-20000000000000000000000000000002-22-2000000
χ20222222222-222-22-2-222222222-2-2-222-2-22-2200000000-2-2000000000000000000000000000000-22-22000000
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
χ31222-22-2-2-22-200202-202-2-22-2-2200-2002-202000002−22−200000000002−22−22−22−2002i−2i002i−2i0000000000−i2i2−i2i200
χ32222-22-2-2-22-200202-202-2-22-2-2200-2002-202000002−22−200000000002−22−22−22−200−2i2i00−2i2i0000000000i2−i2i2−i200
χ33222-22-2-2-22-200202-202-2-22-2-2200-2002-20200000−22−220000000000−22−22−22−22002i−2i002i−2i0000000000i2−i2i2−i200
χ34222-22-2-2-22-200202-202-2-22-2-2200-2002-20200000−22−220000000000−22−22−22−2200−2i2i00−2i2i0000000000−i2i2−i2i200
χ352-222-2-2-2222-2222-2-2-2-2-2-2222-2-222-2-2-2-222200000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ362-222-2-2-2222-2222-2-2-2-2-2-2222-2-222-2-2-2-222200000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ372-222-2-2-222-22-2-2-2222-2-2-2222-2-22-22222-2-2-200000000-220000000000000000000000000000002i−2i−2i2i000000
χ382-222-2-2-222-22-2-2-2222-2-2-2222-2-22-22222-2-2-200000000-22000000000000000000000000000000−2i2i2i−2i000000
χ392-222-2-2-222-2-22-2222-2-2-2-2222-22-2-2-2-2222-222i−2i−2i2i00002-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ402-222-2-2-222-2-22-2222-2-2-2-2222-22-2-2-2-2222-22−2i2i2i−2i00002-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ412-222-2-2-22-122-22-2-2-22111-1-1-112-2-1-1-1111-1122-2-22i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii000000002i−2i−i−iii0000000000
χ422-222-2-2-22-122-22-2-2-22111-1-1-112-2-1-1-1111-1122-2-2−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i00000000−2i2iii−i−i0000000000
χ432-222-2-2-22-122-22-2-2-22111-1-1-112-2-1-1-1111-11-2-2222i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii00000000−2i2iii−i−i0000000000
χ442-222-2-2-22-122-22-2-2-22111-1-1-112-2-1-1-1111-11-2-222−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i000000002i−2i−i−iii0000000000
χ452-222-2-2-22-1-2-22-2222-2111-1-1-112-2111-1-1-11-12i−2i−2i2i0000-11−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i30000000000−333−30000000000
χ462-222-2-2-22-1-2-22-2222-2111-1-1-112-2111-1-1-11-12i−2i−2i2i0000-11−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300000000003−3−330000000000
χ472-222-2-2-22-1-2-22-2222-2111-1-1-112-2111-1-1-11-1−2i2i2i−2i0000-11ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300000000003−3−330000000000
χ482-222-2-2-22-1-2-22-2222-2111-1-1-112-2111-1-1-11-1−2i2i2i−2i0000-11ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i30000000000−333−30000000000
χ492-22-2-222-22-20020-220-2222-2-2-200-200-220200000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2002-200-220000000000−i2i2i2−i200
χ502-22-2-222-22-20020-220-2222-2-2-200-200-220200000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i200-22002-20000000000i2−i2−i2i200
χ512-22-2-222-22-20020-220-2222-2-2-200-200-220200000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2002-200-220000000000i2−i2−i2i200
χ522-22-2-222-22-20020-220-2222-2-2-200-200-220200000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i200-22002-20000000000−i2i2i2−i200
χ5344444444-24-4-44-444-4-2-2-2-2-2-2-2-4-4-222-2-22-2200000000220000000000000000000000000000000000000000
χ5444444444-2-444-44-4-44-2-2-2-2-2-2-2-4-42-2-222-22-200000000220000000000000000000000000000000000000000
χ55444-44-4-4-44400-40-4404-4-44-4-4400400-440-4000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-2400-40-440-222-222-200-2002-20200000000000000000006−6−666−6−66000000000000000000000000
χ57444-44-4-4-4-2400-40-440-222-222-200-2002-2020000000000000000000−666−6−666−6000000000000000000000000
χ58444-44-4-4-4-2-400404-40-222-222-200200-220-20000022−2222−220000000000−22−22−22−22000000000000000000000000
χ59444-44-4-4-4-2-400404-40-222-222-200200-220-200000−2222−222200000000002−22−22−22−2000000000000000000000000
χ6044-44-44-4-440000000044-4-44-4-400000000000000000000000000000000000022−220022−22000000000000000000
χ6144-44-44-4-440000000044-4-44-4-4000000000000000000000000000000000000−222200−2222000000000000000000
χ6244-4-4-4-44440440-400-44-44-4-44-40004-40040-400000000000000000000000000000000000000000000000000
χ6344-4-4-4-44440-4-4040044-44-4-44-4000-4400-40400000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-20440-400-4-22-222-22000-2200-2020000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000000000000
χ6544-4-4-4-444-20440-400-4-22-222-22000-2200-2020000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000000000000
χ6644-4-4-4-444-20-4-404004-22-222-220002-20020-200000000006−6−666−6−6600000000000000000000000000000000
χ6744-4-4-4-444-20-4-404004-22-222-220002-20020-20000000000−666−6−666−600000000000000000000000000000000
χ684-444-4-4-44-24-4444-4-4-4222-2-2-22-44-22222-2-2-2000000002-20000000000000000000000000000000000000000
χ694-444-4-4-44-2-44-4-4-4444222-2-2-22-442-2-2-2-2222000000002-20000000000000000000000000000000000000000
χ704-44-4-444-44400-404-40-4444-4-4-4004004-40-4000000000000000000000000000000000000000000000000000
χ714-44-4-444-4-2400-404-402-2-2-222200-200-22020000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ724-44-4-444-4-2400-404-402-2-2-222200-200-22020000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ734-44-4-444-4-2-40040-4402-2-2-2222002002-20-200000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ744-44-4-444-4-2-40040-4402-2-2-2222002002-20-2000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ754-4-444-44-4400000000-4-44-44-44000000000000000000000000000000000000−2i22i2002i2−2i2000000000000000000
χ764-4-444-44-4400000000-4-44-44-440000000000000000000000000000000000002i2−2i200−2i22i2000000000000000000
χ774-4-4-444-44404-40400-4-44-4-4-4440004-400-40400000000000000000000000000000000000000000000000000
χ784-4-4-444-4440-440-4004-44-4-4-444000-440040-400000000000000000000000000000000000000000000000000
χ794-4-4-444-44-204-40400-42-2222-2-2000-220020-20000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ804-4-4-444-44-204-40400-42-2222-2-2000-220020-20000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ814-4-4-444-44-20-440-40042-2222-2-20002-200-20200000000006−6−66−666−600000000000000000000000000000000
χ824-4-4-444-44-20-440-40042-2222-2-20002-200-2020000000000−666−66−6−6600000000000000000000000000000000
χ8388-88-88-8-8-400000000-4-444-444000000000000000000000000000000000000000000000000000000000000
χ848-8-888-88-8-40000000044-44-44-4000000000000000000000000000000000000000000000000000000000000

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