Finite Group Databasebeta

← Group #10827573

Character table — Group #10827573

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666644444412121212121212122244488881212121212121212121224242424242424242244444661212222444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-1-1
χ41111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111
χ5111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-1-11111-1-1-1-111-1
χ6111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-11-1-1-1-11111-1-11
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11-1-111-1-1-111-1-111-1-11
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111111-1-111-1-111-1
χ911111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1
χ1111111111111111111111-1-1-1-11111111111-1-11-1-11111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-11-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-111-1-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-111-1-11-1-111-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-11-1-111-1-1-1-1-111-1-1111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11111111-1-111-1-1-1
χ17222222222-2-2-2-222222220000222222-2-2-2-200-20000000000-2-200000000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-222222220000222222-2-2-2-200-20000000000-2-2000000000000-2-2222200000-200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200200000000002200000000000022-2-22200000-200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2002000000000022000000000000-2-222-2-200000200000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-122-2-2-2-2-222-1-1-1-1111111-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-2-222-2-2-1-1-1-11111111111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1222-2-2-2-2-2-21111-1-11111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22-2-222221111-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-22222-2-2111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
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
χ2922-22-2-22-222-22-22-2-2-222-22i2i−2i−2i00000022-2-20000000002i2i−2i−2i000000000000000000000000002-20000002i−2i0
χ3022-22-2-22-222-22-22-2-2-222-22i2i−2i−2i00000022-2-20000000002i2i−2i−2i00000000000000000000000000-22000000−2i2i0
χ3122-22-2-22-222-22-22-2-2-222-2−2i−2i2i2i00000022-2-2000000000−2i−2i2i2i000000000000000000000000002-2000000−2i2i0
χ3222-22-2-22-222-22-22-2-2-222-2−2i−2i2i2i00000022-2-2000000000−2i−2i2i2i00000000000000000000000000-220000002i−2i0
χ332-22-2-222-2222-2-2-222-2-22-22i−2i2i−2i0000002-22-22-2000002i−2i2i−2i2i−2i0000002i2i−2i−2i000000000002-200000000000000
χ342-22-2-222-2222-2-2-222-2-22-22i−2i2i−2i0000002-22-2-2200000−2i2i2i−2i2i−2i000000−2i−2i2i2i00000000000-2200000000000000
χ352-22-2-222-2222-2-2-222-2-22-2−2i2i−2i2i0000002-22-22-200000−2i2i−2i2i−2i2i000000−2i−2i2i2i000000000002-200000000000000
χ362-22-2-222-2222-2-2-222-2-22-2−2i2i−2i2i0000002-22-2-22000002i−2i−2i2i−2i2i0000002i2i−2i−2i00000000000-2200000000000000
χ372-22-2-222-2-122-2-21-1-111-112i−2i2i−2i0033−3−3-11-112-2000002i−2i−ii−ii3−3−i3−i3i3i3−i−iii−i3−i3i3i30000000-113−3000000000000
χ382-22-2-222-2-122-2-21-1-111-112i−2i2i−2i0033−3−3-11-11-2200000−2i2i−ii−ii3−3−i3−i3i3i3ii−i−ii3i3−i3−i300000001-1−33000000000000
χ392-22-2-222-2-122-2-21-1-111-112i−2i2i−2i00−3−333-11-112-2000002i−2i−ii−ii−33i3i3−i3−i3−i−iiii3i3−i3−i30000000-11−33000000000000
χ402-22-2-222-2-122-2-21-1-111-112i−2i2i−2i00−3−333-11-11-2200000−2i2i−ii−ii−33i3i3−i3−i3ii−i−i−i3−i3i3i300000001-13−3000000000000
χ412-22-2-222-2-122-2-21-1-111-11−2i2i−2i2i0033−3−3-11-112-200000−2i2ii−ii−i3−3i3i3−i3−i3ii−i−ii3i3−i3−i30000000-113−3000000000000
χ422-22-2-222-2-122-2-21-1-111-11−2i2i−2i2i0033−3−3-11-11-22000002i−2ii−ii−i3−3i3i3−i3−i3−i−iii−i3−i3i3i300000001-1−33000000000000
χ432-22-2-222-2-122-2-21-1-111-11−2i2i−2i2i00−3−333-11-112-200000−2i2ii−ii−i−33−i3−i3i3i3ii−i−i−i3−i3i3i30000000-11−33000000000000
χ442-22-2-222-2-122-2-21-1-111-11−2i2i−2i2i00−3−333-11-11-22000002i−2ii−ii−i−33−i3−i3i3i3−i−iiii3i3−i3−i300000001-13−3000000000000
χ452-2-2-22-22222-2-22-2-2-22-2222-2-220000002-2-220000000002-2-22000000000000002-22-200000000002-20000000
χ462-2-2-22-22222-2-22-2-2-22-2222-2-220000002-2-220000000002-2-2200000000000000-22-220000000000-220000000
χ472-2-2-22-22222-2-22-2-2-22-222-222-20000002-2-22000000000-222-2000000000000002-22-20000000000-220000000
χ482-2-2-22-22222-2-22-2-2-22-222-222-20000002-2-22000000000-222-200000000000000-22-2200000000002-20000000
χ492-2-2-22-2222-222-2-2-2-22-2220000000000-222-20002-200000000002-22-2000000002-2-220000000000002-200000
χ502-2-2-22-2222-222-2-2-2-22-2220000000000-222-20002-200000000002-22-200000000-222-2000000000000-2200000
χ512-2-2-22-2222-222-2-2-2-22-2220000000000-222-2000-220000000000-22-22000000002-2-22000000000000-2200000
χ522-2-2-22-2222-222-2-2-2-22-2220000000000-222-2000-220000000000-22-2200000000-222-20000000000002-200000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-2-2-2-2222200-400000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4222222220040000000000-2-200000000000000000000000000000000000
χ55444-4-4-4-444000044-44-4-4-40000000000000000000000000000000000000000000004i−4i00000000000000000
χ56444-4-4-4-444000044-44-4-4-4000000000000000000000000000000000000000000000−4i4i00000000000000000
χ5744-44-4-44-44-44-444-4-4-444-40000000000-4-44400000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-24-44-4-2222-2-224i4i−4i−4i000000-2-222000000000−2i−2i2i2i0000000000000000000000000000000000000
χ5944-44-4-44-4-24-44-4-2222-2-22−4i−4i4i4i000000-2-2220000000002i2i−2i−2i0000000000000000000000000000000000000
χ6044-44-4-44-4-2-44-44-2222-2-22000000000022-2-2000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ6144-44-4-44-4-2-44-44-2222-2-22000000000022-2-20000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ6244-4-444-4-4400004-44-4-4-440000000000000000000−2i22i20000000000000000−2i22i2−2i22i200000000000000000000000
χ6344-4-444-4-4400004-44-4-4-4400000000000000000002i2−2i200000000000000002i2−2i22i2−2i200000000000000000000000
χ6444-4-444-4-4-20000-22-2222-200000023−2323−23000000000−2i22i2000000000000i6−i6i6−i6i2−i2i2−i200000000000000000000000
χ6544-4-444-4-4-20000-22-2222-200000023−2323−230000000002i2−2i2000000000000−i6i6−i6i6−i2i2−i2i200000000000000000000000
χ6644-4-444-4-4-20000-22-2222-2000000−2323−2323000000000−2i22i2000000000000−i6i6−i6i6i2−i2i2−i200000000000000000000000
χ6744-4-444-4-4-20000-22-2222-2000000−2323−23230000000002i2−2i2000000000000i6−i6i6−i6−i2i2−i2i200000000000000000000000
χ684-4444-4-4-440000-44-4-44-4400000000000000000000000000000000000000000000000000000000000−2i22i2000
χ694-4444-4-4-440000-44-4-44-44000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ704-44-4-444-44-4-444-444-4-44-40000000000-44-4400000000000000000000000000000000000000000000000000
χ714-44-4-444-4-2-4-4442-2-222-220000002323−23−232-22-20000000000000−232300000000000000000000000000000000000
χ724-44-4-444-4-2-4-4442-2-222-22000000−23−2323232-22-2000000000000023−2300000000000000000000000000000000000
χ734-4-44-44-4440000-4-4444-4-400004-44-4-44000000000000000000000000000000000000000000000000000000
χ744-4-44-44-4440000-4-4444-4-40000-44-444-4000000000000000000000000000000000000000000000000000000
χ754-4-44-44-44-2000022-2-2-22200004-4-222-2000000000000000000000006−6−66−666−600000000000000000000000
χ764-4-44-44-44-2000022-2-2-22200004-4-222-200000000000000000000000−666−66−6−6600000000000000000000000
χ774-4-44-44-44-2000022-2-2-2220000-442-2-22000000000000000000000006−6−666−6−6600000000000000000000000
χ784-4-44-44-44-2000022-2-2-2220000-442-2-2200000000000000000000000−666−6−666−600000000000000000000000
χ794-4-4-44-444-24-4-44222-22-2-24-4-44000000-222-2000000000-222-20000000000000000000000000000000000000
χ804-4-4-44-444-24-4-44222-22-2-2-444-4000000-222-20000000002-2-220000000000000000000000000000000000000
χ814-4-4-44-444-2-444-4222-22-2-200000000002-2-220004-40000000000-22-220000000000000000000000000000000
χ824-4-4-44-444-2-444-4222-22-2-200000000002-2-22000-4400000000002-22-20000000000000000000000000000000
χ83888-8-8-8-88-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000
χ848-8888-8-8-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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