Finite Group Databasebeta

← Group #10840267

Character table — Group #10840267

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666224444666612121212444448888121212121212121212122424242424242424444444412121212244444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-111-1-1-1-1-1
χ4111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1111111-1
χ71111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ911111111111111111111-1-11111-1-1-1-11111-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1111111-1-1-1
χ1011111111111111111111-1-11111-1-1-1-11111-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1111-1-1-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-11-1-111-1-1-1-1-111-1-1111
χ1211111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11111111-1-111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-11111-1-1-1-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-111-1-11-1-1-1-11111-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11-1-111-111-1-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1111-1-11111-1-111-1
χ17222222222-2-2-2-222222222200002222-2-2-2-20000-20000-2-2000000000000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-222222222200002222-2-2-2-20000-20000-2-20000000000000000-2-2222200000-200000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200002000022000000000000000022-2-22200000-200000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2000020000220000000000000000-2-222-2-200000200000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-22-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-222222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-222-222-2-211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-2-2-222111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-2-222-2-2111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ2922-2-2-2-222222-2-22-2-222-2-2002i2i−2i−2i00002-22-2000000000002i2i−2i−2i000000000000000000000000002-2002i−2i000
χ3022-2-2-2-222222-2-22-2-222-2-2002i2i−2i−2i00002-22-2000000000002i2i−2i−2i00000000000000000000000000-2200−2i2i000
χ3122-2-2-2-222222-2-22-2-222-2-200−2i−2i2i2i00002-22-200000000000−2i−2i2i2i000000000000000000000000002-200−2i2i000
χ3222-2-2-2-222222-2-22-2-222-2-200−2i−2i2i2i00002-22-200000000000−2i−2i2i2i00000000000000000000000000-22002i−2i000
χ332-22-22-22-222-2-22-22-22-22-2002i−2i2i−2i00002-2-22000000000002i−2i2i−2i0000000000002-22-20000000000002i−2i00000
χ342-22-22-22-222-2-22-22-22-22-2002i−2i2i−2i00002-2-22000000000002i−2i2i−2i000000000000-22-22000000000000−2i2i00000
χ352-22-22-22-222-2-22-22-22-22-200−2i2i−2i2i00002-2-2200000000000−2i2i−2i2i0000000000002-22-2000000000000−2i2i00000
χ362-22-22-22-222-2-22-22-22-22-200−2i2i−2i2i00002-2-2200000000000−2i2i−2i2i000000000000-22-220000000000002i−2i00000
χ372-22-22-22-22-222-2-22-22-22-20000000000-222-22i−2i00000000000002i2i−2i−2i000000002-2-22000000002i−2i000000000
χ382-22-22-22-22-222-2-22-22-22-20000000000-222-22i−2i00000000000002i2i−2i−2i00000000-222-200000000−2i2i000000000
χ392-22-22-22-22-222-2-22-22-22-20000000000-222-2−2i2i0000000000000−2i−2i2i2i000000002-2-2200000000−2i2i000000000
χ402-22-22-22-22-222-2-22-22-22-20000000000-222-2−2i2i0000000000000−2i−2i2i2i00000000-222-2000000002i−2i000000000
χ412-2-22-222-222-22-2-2-222-2-22002-2-22000022-2-2002i−2i02i−2i00002-2-2200002i2i−2i−2i000000000002i−2i00000000000000
χ422-2-22-222-222-22-2-2-222-2-22002-2-22000022-2-200−2i2i0−2i2i00002-2-220000−2i−2i2i2i00000000000−2i2i00000000000000
χ432-2-22-222-222-22-2-2-222-2-2200-222-2000022-2-2002i−2i0−2i2i0000-222-20000−2i−2i2i2i000000000002i−2i00000000000000
χ442-2-22-222-222-22-2-2-222-2-2200-222-2000022-2-200−2i2i02i−2i0000-222-200002i2i−2i−2i00000000000−2i2i00000000000000
χ452-2-22-222-2-12-22-211-1-111-1002-2-22−i3−i3i3i3-1-111002i−2i02i−2i00−i3i3-111-1−i3i3−i3i3−i−iii33−3−30000000−ii3−3000000000000
χ462-2-22-222-2-12-22-211-1-111-1002-2-22−i3−i3i3i3-1-11100−2i2i0−2i2i00−i3i3-111-1−i3i3−i3i3ii−i−i−3−3330000000i−i−33000000000000
χ472-2-22-222-2-12-22-211-1-111-1002-2-22i3i3−i3−i3-1-111002i−2i02i−2i00i3−i3-111-1i3−i3i3−i3−i−iii−3−3330000000−ii−33000000000000
χ482-2-22-222-2-12-22-211-1-111-1002-2-22i3i3−i3−i3-1-11100−2i2i0−2i2i00i3−i3-111-1i3−i3i3−i3ii−i−i33−3−30000000i−i3−3000000000000
χ492-2-22-222-2-12-22-211-1-111-100-222-2−i3−i3i3i3-1-111002i−2i0−2i2i00−i3i31-1-11i3−i3i3−i3ii−i−i−3−3330000000−ii3−3000000000000
χ502-2-22-222-2-12-22-211-1-111-100-222-2−i3−i3i3i3-1-11100−2i2i02i−2i00−i3i31-1-11i3−i3i3−i3−i−iii33−3−30000000i−i−33000000000000
χ512-2-22-222-2-12-22-211-1-111-100-222-2i3i3−i3−i3-1-111002i−2i0−2i2i00i3−i31-1-11−i3i3−i3i3ii−i−i33−3−30000000−ii−33000000000000
χ522-2-22-222-2-12-22-211-1-111-100-222-2i3i3−i3−i3-1-11100−2i2i02i−2i00i3−i31-1-11−i3i3−i3i3−i−iii−3−3330000000i−i3−3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-222220000-4000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222000040000-2-2000000000000000000000000000000000000000
χ554444-4-4-4-44000044-4-4-4-444-400004-44-4000000000000000000000000000000000000000000000000000000
χ564444-4-4-4-44000044-4-4-4-44-440000-44-44000000000000000000000000000000000000000000000000000000
χ574444-4-4-4-4-20000-2-22222-24-40000-22-22000000000000000000000006−66−66−66−600000000000000000000000
χ584444-4-4-4-4-20000-2-22222-24-40000-22-2200000000000000000000000−66−66−66−6600000000000000000000000
χ594444-4-4-4-4-20000-2-22222-2-4400002-22-2000000000000000000000006−66−6−66−6600000000000000000000000
χ604444-4-4-4-4-20000-2-22222-2-4400002-22-200000000000000000000000−66−666−66−600000000000000000000000
χ6144-4-444-4-4400004-44-4-44-4000000000000000000000000000000000000000000000000000000000000022−220
χ6244-4-444-4-4400004-44-4-44-40000000000000000000000000000000000000000000000000000000000000−22220
χ6344-4-4-4-4444-4-4444-4-444-4-40000000000-44-4400000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-244-4-4-222-2-222004i4i−4i−4i0000-22-2200000000000−2i−2i2i2i00000000000000000000000000000000000
χ6544-4-4-4-444-244-4-4-222-2-22200−4i−4i4i4i0000-22-22000000000002i2i−2i−2i00000000000000000000000000000000000
χ6644-4-4-4-444-2-4-444-222-2-22200000000002-22-200000000000000023−23−23230000000000000000000000000000000
χ6744-4-4-4-444-2-4-444-222-2-22200000000002-22-2000000000000000−232323−230000000000000000000000000000000
χ684-44-44-44-4-24-4-442-22-22-22004i−4i4i−4i0000-222-200000000000−2i2i−2i2i00000000000000000000000000000000000
χ694-44-44-44-4-24-4-442-22-22-2200−4i4i−4i4i0000-222-2000000000002i−2i2i−2i00000000000000000000000000000000000
χ704-44-44-44-4-2-444-42-22-22-2200000000002-2-224i−4i0000000000000−2i−2i2i2i0000000000000000000000000000000
χ714-44-44-44-4-2-444-42-22-22-2200000000002-2-22−4i4i00000000000002i2i−2i−2i0000000000000000000000000000000
χ724-44-4-44-4440000-444-44-4-40000000000000000000000000000000000000000000004i−4i00000000000000000
χ734-44-4-44-4440000-444-44-4-4000000000000000000000000000000000000000000000−4i4i00000000000000000
χ744-4-444-4-4440000-4-4-4-444400000000000000000000022−220000000000000022−22−222200000000000000000000000
χ754-4-444-4-4440000-4-4-4-4444000000000000000000000−222200000000000000−222222−2200000000000000000000000
χ764-4-444-4-44-200002222-2-2-2000000−2i32i32i3−2i30000000000022−220000000000−i6i6i6−i6−222−200000000000000000000000
χ774-4-444-4-44-200002222-2-2-2000000−2i32i32i3−2i300000000000−22220000000000i6−i6−i6i62−2−2200000000000000000000000
χ784-4-444-4-44-200002222-2-2-20000002i3−2i3−2i32i30000000000022−220000000000i6−i6−i6i6−222−200000000000000000000000
χ794-4-444-4-44-200002222-2-2-20000002i3−2i3−2i32i300000000000−22220000000000−i6i6i6−i62−2−2200000000000000000000000
χ804-4-44-444-44-44-44-4-444-4-440000000000-4-44400000000000000000000000000000000000000000000000000
χ814-4-44-444-4-2-44-4422-2-222-2000000−2i3−2i32i32i322-2-20000000002i3−2i3000000000000000000000000000000000000000
χ824-4-44-444-4-2-44-4422-2-222-20000002i32i3−2i3−2i322-2-2000000000−2i32i3000000000000000000000000000000000000000
χ8388-8-888-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-88-88-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000

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