Finite Group Databasebeta

← Group #10827610

Character table — Group #10827610

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666644444412121212121212122244488881212121212121212121224242424242424242222444661212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ41111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1111111-1
χ71111111111111111111111-1-1-1-111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ911111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-11111-1-1-1-1-111-1
χ1011111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-111111-1-11
χ1111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-111-1-111-1-1-111-1-11
χ1211111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-1-11111-1-1111-1-111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-111-1-1-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1-1-1111-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-111-1-1-1-1-111-1-1111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-11111111-1-111-1-1-1
χ17222222222-2-2-2-222222222200002222-2-2-2-200-2000000-2-2000000000000000022-2-2-2-200000000020000000
χ18222222222-2-2-2-222222222200002222-2-2-2-200-2000000-2-20000000000000000-2-22222000000000-20000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-20020000002200000000000000002222-2-2000000000-20000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000220000000000000000-2-2-2-22200000000020000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-22-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-122-2-2-2-2-22211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-2-222-2-211-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-22222-2-2111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2-2-222-2-222111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ2922-22-2-22-222-22-22-2-2-222-2002i2i−2i−2i000022-2-2000000000002i2i−2i−2i000000000000000000000002-200000002i−2i0
χ3022-22-2-22-222-22-22-2-2-222-2002i2i−2i−2i000022-2-2000000000002i2i−2i−2i00000000000000000000000-220000000−2i2i0
χ3122-22-2-22-222-22-22-2-2-222-200−2i−2i2i2i000022-2-200000000000−2i−2i2i2i000000000000000000000002-20000000−2i2i0
χ3222-22-2-22-222-22-22-2-2-222-200−2i−2i2i2i000022-2-200000000000−2i−2i2i2i00000000000000000000000-2200000002i−2i0
χ332-22-22-22-2222-2-2-222-2-22-2002i−2i2i−2i00002-22-22-2000002i−2i002i−2i2i−2i00002i2i−2i−2i000000000002-200000000000000
χ342-22-22-22-2222-2-2-222-2-22-2002i−2i2i−2i00002-22-2-2200000−2i2i002i−2i2i−2i0000−2i−2i2i2i00000000000-2200000000000000
χ352-22-22-22-2222-2-2-222-2-22-200−2i2i−2i2i00002-22-22-200000−2i2i00−2i2i−2i2i0000−2i−2i2i2i000000000002-200000000000000
χ362-22-22-22-2222-2-2-222-2-22-200−2i2i−2i2i00002-22-2-22000002i−2i00−2i2i−2i2i00002i2i−2i−2i00000000000-2200000000000000
χ372-22-22-22-2-122-2-21-1-111-11002i−2i2i−2i33−3−3-11-112-2000002i−2i3−3−ii−ii−i3−i3i3i3−i−iii−i3−i3i3i30000000-113−3000000000000
χ382-22-22-22-2-122-2-21-1-111-11002i−2i2i−2i33−3−3-11-11-2200000−2i2i3−3−ii−ii−i3−i3i3i3ii−i−ii3i3−i3−i300000001-1−33000000000000
χ392-22-22-22-2-122-2-21-1-111-11002i−2i2i−2i−3−333-11-112-2000002i−2i−33−ii−iii3i3−i3−i3−i−iiii3i3−i3−i30000000-11−33000000000000
χ402-22-22-22-2-122-2-21-1-111-11002i−2i2i−2i−3−333-11-11-2200000−2i2i−33−ii−iii3i3−i3−i3ii−i−i−i3−i3i3i300000001-13−3000000000000
χ412-22-22-22-2-122-2-21-1-111-1100−2i2i−2i2i33−3−3-11-112-200000−2i2i3−3i−ii−ii3i3−i3−i3ii−i−ii3i3−i3−i30000000-113−3000000000000
χ422-22-22-22-2-122-2-21-1-111-1100−2i2i−2i2i33−3−3-11-11-22000002i−2i3−3i−ii−ii3i3−i3−i3−i−iii−i3−i3i3i300000001-1−33000000000000
χ432-22-22-22-2-122-2-21-1-111-1100−2i2i−2i2i−3−333-11-112-200000−2i2i−33i−ii−i−i3−i3i3i3ii−i−i−i3−i3i3i30000000-11−33000000000000
χ442-22-22-22-2-122-2-21-1-111-1100−2i2i−2i2i−3−333-11-11-22000002i−2i−33i−ii−i−i3−i3i3i3−i−iiii3i3−i3−i300000001-13−3000000000000
χ452-2-2-2-222222-2-22-2-2-22-222002-2-2200002-2-22000000000002-2-220000000000002-2002-200000002-200000000
χ462-2-2-2-222222-2-22-2-2-22-222002-2-2200002-2-22000000000002-2-22000000000000-2200-220000000-2200000000
χ472-2-2-2-222222-2-22-2-2-22-22200-222-200002-2-2200000000000-222-20000000000002-2002-20000000-2200000000
χ482-2-2-2-222222-2-22-2-2-22-22200-222-200002-2-2200000000000-222-2000000000000-2200-2200000002-200000000
χ492-2-2-2-22222-222-2-2-2-22-2220000000000-222-20002-200000000002-22-2000000002-200-2200000000002-200000
χ502-2-2-2-22222-222-2-2-2-22-2220000000000-222-20002-200000000002-22-200000000-22002-20000000000-2200000
χ512-2-2-2-22222-222-2-2-2-22-2220000000000-222-2000-220000000000-22-22000000002-200-220000000000-2200000
χ522-2-2-2-22222-222-2-2-2-22-2220000000000-222-2000-220000000000-22-2200000000-22002-200000000002-200000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-2222200-400000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222004000000-2-2000000000000000000000000000000000000000
χ55444-4-4-4-444000044-4-4-4-444i−4i00004i−4i4i−4i000000000000000000000000000000000000000000000000000000
χ56444-4-4-4-444000044-4-4-4-44−4i4i0000−4i4i−4i4i000000000000000000000000000000000000000000000000000000
χ57444-4-4-4-44-20000-2-22222-24i−4i0000−2i2i−2i2i00000000000000000000000i6−i6i6−i66−66−600000000000000000000000
χ58444-4-4-4-44-20000-2-22222-24i−4i0000−2i2i−2i2i00000000000000000000000−i6i6−i6i6−66−6600000000000000000000000
χ59444-4-4-4-44-20000-2-22222-2−4i4i00002i−2i2i−2i00000000000000000000000i6−i6i6−i6−66−6600000000000000000000000
χ60444-4-4-4-44-20000-2-22222-2−4i4i00002i−2i2i−2i00000000000000000000000−i6i6−i6i66−66−600000000000000000000000
χ6144-44-4-44-44-44-444-4-4-444-40000000000-4-44400000000000000000000000000000000000000000000000000
χ6244-44-4-44-4-24-44-4-2222-2-22004i4i−4i−4i0000-2-22200000000000−2i−2i2i2i00000000000000000000000000000000000
χ6344-44-4-44-4-24-44-4-2222-2-2200−4i−4i4i4i0000-2-222000000000002i2i−2i−2i00000000000000000000000000000000000
χ6444-44-4-44-4-2-44-44-2222-2-22000000000022-2-2000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ6544-44-4-44-4-2-44-44-2222-2-22000000000022-2-20000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ6644-4-444-4-4400004-444-4-4-400000000000000000000000000000000000000000000000000000000000−2i22i2000
χ6744-4-444-4-4400004-444-4-4-4000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ684-444-44-4-440000-44-444-4-40000000000000000000−2i22i20000000000000000−2i22i22i2−2i200000000000000000000000
χ694-444-44-4-440000-44-444-4-400000000000000000002i2−2i200000000000000002i2−2i2−2i22i200000000000000000000000
χ704-444-44-4-4-200002-22-2-222000000−2i32i32i3−2i3000000000−2i22i2000000000000−666−6i2−i2−i2i200000000000000000000000
χ714-444-44-4-4-200002-22-2-222000000−2i32i32i3−2i30000000002i2−2i20000000000006−6−66−i2i2i2−i200000000000000000000000
χ724-444-44-4-4-200002-22-2-2220000002i3−2i3−2i32i3000000000−2i22i20000000000006−6−66i2−i2−i2i200000000000000000000000
χ734-444-44-4-4-200002-22-2-2220000002i3−2i3−2i32i30000000002i2−2i2000000000000−666−6−i2i2i2−i200000000000000000000000
χ744-44-44-44-44-4-444-444-4-44-40000000000-44-4400000000000000000000000000000000000000000000000000
χ754-44-44-44-4-2-4-4442-2-222-220000002323−23−232-22-2000000000−2323000000000000000000000000000000000000000
χ764-44-44-44-4-2-4-4442-2-222-22000000−23−2323232-22-200000000023−23000000000000000000000000000000000000000
χ774-4-444-4-4440000-4-44-44-4400000000000000000000000000000000000000000004-40000000000000000000
χ784-4-444-4-4440000-4-44-44-440000000000000000000000000000000000000000000-440000000000000000000
χ794-4-4-4-4444-24-4-44222-22-2-2004-4-440000-222-200000000000-222-200000000000000000000000000000000000
χ804-4-4-4-4444-24-4-44222-22-2-200-444-40000-222-2000000000002-2-2200000000000000000000000000000000000
χ814-4-4-4-4444-2-444-4222-22-2-200000000002-2-220004-40000000000-22-220000000000000000000000000000000
χ824-4-4-4-4444-2-444-4222-22-2-200000000002-2-22000-4400000000002-22-20000000000000000000000000000000
χ8388-8-888-8-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000

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