Finite Group Databasebeta

← Group #10691397

Character table — Group #10691397

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212888888881212242424242424242424242424242424248888888844121212122244888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ91-1-1-11-1111111-11-1-1-1-1-1-1111-11-1111-1-1-11-111-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−iii−i−iii−i−ii−iii−i−i1-11-1ii−i−i1-1
χ101-1-1-11-1111111-11-1-1-1-1-1-1111-11-1111-1-1-11-111-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i−i−iii−i−iiii−iii−i−i-11-11−i−iii-11
χ111-1-1-11-1111111-11-1-1-1-1-1-1111-11-1111-1-1-11-111-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiiiii−i−iii−i−i−ii−i−iii-11-11ii−i−i-11
χ121-1-1-11-1111111-11-1-1-1-1-1-1111-11-1111-1-1-11-111-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii−ii−i−iii1-11-1−i−iii1-1
χ131-1-1-11-1111111-11-1-1-1-1-1-1111-11-1111-1-1-11-1-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−iii−i−iii−i−i−ii−i−iii1-11-1−i−iii-11
χ141-1-1-11-1111111-11-1-1-1-1-1-1111-11-1111-1-1-11-1-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−i−i−iii−i−iii−ii−i−iii-11-11ii−i−i1-1
χ151-1-1-11-1111111-11-1-1-1-1-1-1111-11-1111-1-1-11-1-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiiiii−i−iii−i−ii−iii−i−i-11-11−i−iii1-1
χ161-1-1-11-1111111-11-1-1-1-1-1-1111-11-1111-1-1-11-1-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiii−i−iii−i−iiii−iii−i−i1-11-1ii−i−i-11
χ1722222222222-2-2-222-22222222-2-222-22-2-2-2200000000-2-200000000000000002222-2-2-2-20000000000000000
χ1822222222222-2-2-222-22222222-2-222-22-2-2-2200000000-2-20000000000000000-2-2-2-222220000000000000000
χ19222222222-2-2222-2-222222222-2-2-2-22-2222-200000000-2-200000000000000000000000000000022-2-2000000
χ20222222222-2-2222-2-222222222-2-2-2-22-2222-200000000-2-2000000000000000000000000000000-2-222000000
χ21222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200002i−2i2i−2i22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ22222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000−2i2i−2i2i2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
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
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100002i−2i2i−2i-1-133−3−333−3−3−i−iii−i−iii0000000000−i3i3−i3i30000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100002i−2i2i−2i-1-1−3−333−3−333−i−iii−i−iii0000000000i3−i3i3−i30000000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111110000−2i2i−2i2i-1-133−3−333−3−3ii−i−iii−i−i0000000000i3−i3i3−i30000000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111110000−2i2i−2i2i-1-1−3−333−3−333ii−i−iii−i−i0000000000−i3i3−i3i30000000000
χ31222-2-2-22-222-2000-22022-22-2-2-2002-20-20002−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i20000000000002-22-20000000000−i2i2−i2i200
χ32222-2-2-22-222-2000-22022-22-2-2-2002-20-20002−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2000000000000-22-220000000000i2−i2i2−i200
χ33222-2-2-22-222-2000-22022-22-2-2-2002-20-20002i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i20000000000002-22-20000000000i2−i2i2−i200
χ34222-2-2-22-222-2000-22022-22-2-2-2002-20-20002i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2000000000000-22-220000000000−i2i2−i2i200
χ352-2-22-222-222-20002-20-2-222-2-22002-202000-2−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i20000000000002i−2i−2i2i00000000002−2−2200
χ362-2-22-222-222-20002-20-2-222-2-22002-202000-2−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i2000000000000−2i2i2i−2i0000000000−222−200
χ372-2-22-222-222-20002-20-2-222-2-22002-202000-2i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i20000000000002i−2i−2i2i0000000000−222−200
χ382-2-22-222-222-20002-20-2-222-2-22002-202000-2i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i2000000000000−2i2i2i−2i00000000002−2−2200
χ392-2-2-22-222222-22-2-2-22-2-2-2222-2-2222-2-222-2-200000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402-2-2-22-222222-22-2-2-22-2-2-2222-2-2222-2-222-2-200000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412-2-2-22-2222-2-22-2222-2-2-2-2222-2-22-2-222-2-22200000000-220000000000000000000000000000002-2-22000000
χ422-2-2-22-2222-2-22-2222-2-2-2-2222-2-22-2-222-2-22200000000-22000000000000000000000000000000-222-2000000
χ432-2-2-22-2222-2-2-22-2222-2-2-2222-22-2-2-2-2222-2200002-2-222-20000000022-2-2-2-222000000000000000000000000
χ442-2-2-22-2222-2-2-22-2222-2-2-2222-22-2-2-2-2222-220000-222-22-200000000-2-22222-2-2000000000000000000000000
χ452-2-2-22-222-1222-22-2-2-2111-1-1-112-2-1-1-1111-1122-2-22i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii000000002i−2i−i−iii0000000000
χ462-2-2-22-222-1222-22-2-2-2111-1-1-112-2-1-1-1111-1122-2-2−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i00000000−2i2iii−i−i0000000000
χ472-2-2-22-222-1222-22-2-2-2111-1-1-112-2-1-1-1111-11-2-2222i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii00000000−2i2iii−i−i0000000000
χ482-2-2-22-222-1222-22-2-2-2111-1-1-112-2-1-1-1111-11-2-222−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i000000002i−2i−i−iii0000000000
χ492-2-2-22-222-1-2-2-22-2222111-1-1-112-2111-1-1-11-100002-2-22-1133−3−3−3−333-1-11111-1-10000000000−333−30000000000
χ502-2-2-22-222-1-2-2-22-2222111-1-1-112-2111-1-1-11-100002-2-22-11−3−33333−3−3-1-11111-1-100000000003−3−330000000000
χ512-2-2-22-222-1-2-2-22-2222111-1-1-112-2111-1-1-11-10000-222-2-1133−3−3−3−33311-1-1-1-11100000000003−3−330000000000
χ522-2-2-22-222-1-2-2-22-2222111-1-1-112-2111-1-1-11-10000-222-2-11−3−33333−3−311-1-1-1-1110000000000−333−30000000000
χ5344444444-244-4-4-444-4-2-2-2-2-2-2-2-4-4-2-22-2222-200000000220000000000000000000000000000000000000000
χ5444444444-2-4-4444-4-44-2-2-2-2-2-2-2-4-422-22-2-2-2200000000220000000000000000000000000000000000000000
χ55444-4-4-44-44-440004-4044-44-4-4-400-4404000-400000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-24-4000-440-2-22-222200-2202000-2−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000
χ57444-4-4-44-4-24-4000-440-2-22-222200-2202000-22i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000
χ58444-4-4-44-4-2-440004-40-2-22-2222002-20-200020000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ59444-4-4-44-4-2-440004-40-2-22-2222002-20-200020000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ6044-444-4-4-44000000004-44-44-4-400000000000000000000000000000000000022−2222−2200000000000000000000
χ6144-444-4-4-44000000004-44-44-4-4000000000000000000000000000000000000−2222−222200000000000000000000
χ6244-4-4-44-444004-4-40044-4-4-4-4440000404-4-4000000000000000000000000000000000000000000000000000
χ6344-4-4-44-44400-44400-44-4-4-4-4440000-40-444000000000000000000000000000000000000000000000000000
χ6444-4-4-44-44-2004-4-4004-22222-2-20000-20-22200000000000000000006−66−66−66−6000000000000000000000000
χ6544-4-4-44-44-2004-4-4004-22222-2-20000-20-2220000000000000000000−66−66−66−66000000000000000000000000
χ6644-4-4-44-44-200-44400-4-22222-2-20000202-2-20000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ6744-4-4-44-44-200-44400-4-22222-2-20000202-2-20000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ684-444-4-4-4440044-400-4-444-4-44-4000040-44-4000000000000000000000000000000000000000000000000000
χ694-444-4-4-44400-4-44004-444-4-44-40000-404-44000000000000000000000000000000000000000000000000000
χ704-444-4-4-44-20044-400-42-2-222-220000-202-220000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ714-444-4-4-44-20044-400-42-2-222-220000-202-220000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ724-444-4-4-44-200-4-440042-2-222-22000020-22-200000000000000000006−6−66−666−6000000000000000000000000
χ734-444-4-4-44-200-4-440042-2-222-22000020-22-20000000000000000000−666−66−6−66000000000000000000000000
χ744-44-444-4-4400000000-44-4-44-44000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ754-44-444-4-4400000000-44-4-44-440000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ764-4-44-444-44-44000-440-4-444-4-4400-440-4000400000000000000000000000000000000000000000000000000
χ774-4-44-444-4-24-40004-4022-2-222-200-220-20002−2i22i22i2−2i2000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000000000
χ784-4-44-444-4-24-40004-4022-2-222-200-220-200022i2−2i2−2i22i2000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000000000
χ794-4-44-444-4-2-44000-44022-2-222-2002-202000-20000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ804-4-44-444-4-2-44000-44022-2-222-2002-202000-20000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000
χ814-4-4-44-444-244-44-4-4-44222-2-2-22-44-2-222-2-222000000002-20000000000000000000000000000000000000000
χ824-4-4-44-444-2-4-44-4444-4222-2-2-22-4422-2-222-2-2000000002-20000000000000000000000000000000000000000
χ8388-888-8-8-8-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000
χ848-88-888-8-8-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000

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