Finite Group Databasebeta

← Group #10831716

Character table — Group #10831716

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666222244121212121212121244444666688881212121212122424242424242424444444412121212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111
χ5111111111111111111111111-1-111-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111111-1-1-111-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1111-1-1111
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1111
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-111111-1-1-1
χ911111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1111111-1
χ1111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ1211111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-11111-1-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-111-1-1111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1111-1-1-1-1-1-1-11111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111111-1-1-1-111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-2-2000000000000-2-200000000000022-2-222000000000-20000000
χ18222222222-2-2-2-22222222000022-2-22222-2-2-2000000000000-2-2000000000000-2-222-2-200000000020000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-220000000000002200000000000022-2-2-2-200000000020000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2200000000000022000000000000-2-22222000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-222-1-1-1-122-2-2111111-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-2-1-1-1-1-2-2221111111111-1-1-1-10000002-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2221111-2-2-2-2-1-11111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222221111-2-22211-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-2111122-2-211-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ292222-2-2-2-222-22-222-22-2-2-222-2-200220000-2-20000022-2-2000000000000000000000000000002-2000002-2000
χ302222-2-2-2-222-22-222-22-2-2-222-2-200220000-2-20000022-2-200000000000000000000000000000-2200000-22000
χ312222-2-2-2-222-22-222-22-2-2-2-2-22200220000-2-200000-2-222000000000000000000000000000002-200000-22000
χ322222-2-2-2-222-22-222-22-2-2-2-2-22200220000-2-200000-2-22200000000000000000000000000000-22000002-2000
χ332-2-2222-2-22-2-222-2-222-22-22-22-2002-200002-20002i−2i2-22-22i−2i000000002i2i−2i−2i00000000000002i−2i000000000000
χ342-2-2222-2-22-2-222-2-222-22-22-22-2002-200002-2000−2i2i2-22-2−2i2i00000000−2i−2i2i2i0000000000000−2i2i000000000000
χ352-2-2222-2-22-2-222-2-222-22-2-22-22002-200002-20002i−2i-22-22−2i2i00000000−2i−2i2i2i00000000000002i−2i000000000000
χ362-2-2222-2-22-2-222-2-222-22-2-22-22002-200002-2000−2i2i-22-222i−2i000000002i2i−2i−2i0000000000000−2i2i000000000000
χ372-2-2222-2-2-1-2-22211-1-11-112-22-200-1133−3−3-110002i−2i-11-112i−2i003−333−3−3−i−iii−i3−i3i3i30000000−i3i3−ii000000000000
χ382-2-2222-2-2-1-2-22211-1-11-112-22-200-1133−3−3-11000−2i2i-11-11−2i2i003−333−3−3ii−i−ii3i3−i3−i30000000i3−i3i−i000000000000
χ392-2-2222-2-2-1-2-22211-1-11-112-22-200-11−3−333-110002i−2i-11-112i−2i00−33−3−333−i−iiii3i3−i3−i30000000i3−i3−ii000000000000
χ402-2-2222-2-2-1-2-22211-1-11-112-22-200-11−3−333-11000−2i2i-11-11−2i2i00−33−3−333ii−i−i−i3−i3i3i30000000−i3i3i−i000000000000
χ412-2-2222-2-2-1-2-22211-1-11-11-22-2200-1133−3−3-110002i−2i1-11-1−2i2i003−3−3−333ii−i−ii3i3−i3−i30000000−i3i3−ii000000000000
χ422-2-2222-2-2-1-2-22211-1-11-11-22-2200-1133−3−3-11000−2i2i1-11-12i−2i003−3−3−333−i−iii−i3−i3i3i30000000i3−i3i−i000000000000
χ432-2-2222-2-2-1-2-22211-1-11-11-22-2200-11−3−333-110002i−2i1-11-1−2i2i00−3333−3−3ii−i−i−i3−i3i3i30000000i3−i3−ii000000000000
χ442-2-2222-2-2-1-2-22211-1-11-11-22-2200-11−3−333-11000−2i2i1-11-12i−2i00−3333−3−3−i−iiii3i3−i3−i30000000−i3i3i−i000000000000
χ452-2-22-2-22222-2-22-2-2-222-22000000-2200002-202-20000000000002-22-2000000002-22-20000000000002-200000
χ462-2-22-2-22222-2-22-2-2-222-22000000-2200002-202-20000000000002-22-200000000-22-22000000000000-2200000
χ472-2-22-2-22222-2-22-2-2-222-22000000-2200002-20-22000000000000-22-22000000002-22-2000000000000-2200000
χ482-2-22-2-22222-2-22-2-2-222-22000000-2200002-20-22000000000000-22-2200000000-22-220000000000002-200000
χ492-2-22-2-2222-222-2-2-2-222-222-2-22002-20000-22000002-2-220000000000000000002-2-220000000002-200000000
χ502-2-22-2-2222-222-2-2-2-222-222-2-22002-20000-22000002-2-22000000000000000000-222-2000000000-2200000000
χ512-2-22-2-2222-222-2-2-2-222-22-222-2002-20000-2200000-222-20000000000000000002-2-22000000000-2200000000
χ522-2-22-2-2222-222-2-2-2-222-22-222-2002-20000-2200000-222-2000000000000000000-222-20000000002-200000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-222-40000000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4222222224000000000000-2-200000000000000000000000000000000000
χ554444-4-4-4-44-44-4444-44-4-4-4000000-4-400004400000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-24-44-4-2-22-222244-4-400-2-200002200000-2-22200000000000000000000000000000000000000000
χ574444-4-4-4-4-24-44-4-2-22-2222-4-44400-2-20000220000022-2-200000000000000000000000000000000000000000
χ584444-4-4-4-4-2-44-44-2-22-2222000000220000-2-200000000000000023−23−23230000000000000000000000000000000
χ594444-4-4-4-4-2-44-44-2-22-2222000000220000-2-2000000000000000−232323−230000000000000000000000000000000
χ6044-4-44-44-4400004-4-4-444-400004i−4i004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ6144-4-44-44-4400004-4-4-444-40000−4i4i00−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ6244-4-44-44-4-20000-2222-2-2200004i−4i00−2i2i−2i2i0000000000000000000006−66−6i6−i6i6−i600000000000000000000000
χ6344-4-44-44-4-20000-2222-2-2200004i−4i00−2i2i−2i2i000000000000000000000−66−66−i6i6−i6i600000000000000000000000
χ6444-4-44-44-4-20000-2222-2-220000−4i4i002i−2i2i−2i0000000000000000000006−66−6−i6i6−i6i600000000000000000000000
χ6544-4-44-44-4-20000-2222-2-220000−4i4i002i−2i2i−2i000000000000000000000−66−66i6−i6i6−i600000000000000000000000
χ6644-4-4-44-44400004-44-4-4-44000000000000000000000000000000000000000000000000000000000000022−220
χ6744-4-4-44-44400004-44-4-4-440000000000000000000000000000000000000000000000000000000000000−22220
χ684-44-44-4-4440000-44-4-4-444000000000000000000000000022−22000000000022−22−222200000000000000000000000
χ694-44-44-4-4440000-44-4-4-4440000000000000000000000000−22220000000000−222222−2200000000000000000000000
χ704-44-44-4-44-200002-2222-2-200000000−2i32i32i3−2i3000000000000022−22000000i6−i6−i6i6−222−200000000000000000000000
χ714-44-44-4-44-200002-2222-2-200000000−2i32i32i3−2i30000000000000−2222000000−i6i6i6−i62−2−2200000000000000000000000
χ724-44-44-4-44-200002-2222-2-2000000002i3−2i3−2i32i3000000000000022−22000000−i6i6i6−i6−222−200000000000000000000000
χ734-44-44-4-44-200002-2222-2-2000000002i3−2i3−2i32i30000000000000−2222000000i6−i6−i6i62−2−2200000000000000000000000
χ744-44-4-444-440000-444-44-4-40000000000000000000000000000000000000000000004i−4i00000000000000000
χ754-44-4-444-440000-444-44-4-4000000000000000000000000000000000000000000000−4i4i00000000000000000
χ764-4-4444-4-4444-4-4-4-444-44-4000000-440000-4400000000000000000000000000000000000000000000000000
χ774-4-4444-4-4-244-4-422-2-22-220000002-22323−23−232-20000000000000−232300000000000000000000000000000000000
χ784-4-4444-4-4-244-4-422-2-22-220000002-2−23−2323232-2000000000000023−2300000000000000000000000000000000000
χ794-4-44-4-444-24-4-44222-2-22-20000002-20000-2204-4000000000000-22-220000000000000000000000000000000
χ804-4-44-4-444-24-4-44222-2-22-20000002-20000-220-440000000000002-22-20000000000000000000000000000000
χ814-4-44-4-444-2-444-4222-2-22-24-4-4400-2200002-200000-222-200000000000000000000000000000000000000000
χ824-4-44-4-444-2-444-4222-2-22-2-444-400-2200002-2000002-2-2200000000000000000000000000000000000000000
χ8388-8-8-88-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-888-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000

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