Finite Group Databasebeta

← Group #10858397

Character table — Group #10858397

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666644444412121212121212122244488881212121212121212121224242424242424244444444661212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111-1-1-1-1-1-1111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1111-1-1-1-111-1-11
χ6111111111111111111111111-1-1-1-1-1-1111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-1-1-1-11111-1-111-1
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111111-1-111-1-111-1
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-111-1-1-111-1-111-1-11
χ911111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
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
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-11-1-111-1-1-1-1111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-111-1-1-111-1-11111-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11-1-1111-1-1111111-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-1-111-111-1-1-1-1-1-1111
χ17222222222-2-2-2-222222220000222222-2-2-2-200-20000000000-2-20000000000002222-2-200000-200000000000
χ18222222222-2-2-2-222222220000222222-2-2-2-200-20000000000-2-2000000000000-2-2-2-22200000200000000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-122-2-2-222-2-2-1-1-1-1111111-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-2-2-2-222-1-1-1-11111111111-1-1-1-1000000211-1-1000000000000
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
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-222-2-222111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2-2-22222-2-2111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ292222-2-2-2-2222-2-222-2-2-22-222-2-20000002-22-22-20002-20022-2-200000022-2-2000000000002-200000000000000
χ302222-2-2-2-2222-2-222-2-2-22-222-2-20000002-22-2-22000-220022-2-2000000-2-22200000000000-2200000000000000
χ312222-2-2-2-2222-2-222-2-2-22-2-2-2220000002-22-22-2000-2200-2-222000000-2-222000000000002-200000000000000
χ322222-2-2-2-2222-2-222-2-2-22-2-2-2220000002-22-2-220002-200-2-22200000022-2-200000000000-2200000000000000
χ332222-2-2-2-2-122-2-2-1-1111-1122-2-20033−3−3-11-112-20002-200-1-1113−333−3−3-1-11133−3−30000000-113−3000000000000
χ342222-2-2-2-2-122-2-2-1-1111-1122-2-20033−3−3-11-11-22000-2200-1-1113−333−3−311-1-1−3−33300000001-1−33000000000000
χ352222-2-2-2-2-122-2-2-1-1111-1122-2-200−3−333-11-112-20002-200-1-111−33−3−333-1-111−3−3330000000-11−33000000000000
χ362222-2-2-2-2-122-2-2-1-1111-1122-2-200−3−333-11-11-22000-2200-1-111−33−3−33311-1-133−3−300000001-13−3000000000000
χ372222-2-2-2-2-122-2-2-1-1111-11-2-2220033−3−3-11-112-2000-220011-1-13−3−3−33311-1-1−3−3330000000-113−3000000000000
χ382222-2-2-2-2-122-2-2-1-1111-11-2-2220033−3−3-11-11-220002-20011-1-13−3−3−333-1-11133−3−300000001-1−33000000000000
χ392222-2-2-2-2-122-2-2-1-1111-11-2-22200−3−333-11-112-2000-220011-1-1−3333−3−311-1-133−3−30000000-11−33000000000000
χ402222-2-2-2-2-122-2-2-1-1111-11-2-22200−3−333-11-11-220002-20011-1-1−3333−3−3-1-111−3−33300000001-13−3000000000000
χ412-2-222-22-222-2-22-2-22-222-2000000000022-2-20002i−2i00000000002i−2i2i−2i00000000002i−2i2i−2i0000002-2000000000
χ422-2-222-22-222-2-22-2-22-222-2000000000022-2-20002i−2i00000000002i−2i2i−2i0000000000−2i2i−2i2i000000-22000000000
χ432-2-222-22-222-2-22-2-22-222-2000000000022-2-2000−2i2i0000000000−2i2i−2i2i00000000002i−2i2i−2i000000-22000000000
χ442-2-222-22-222-2-22-2-22-222-2000000000022-2-2000−2i2i0000000000−2i2i−2i2i0000000000−2i2i−2i2i0000002-2000000000
χ452-2-222-22-22-222-2-2-22-222-22-22-2000000-2-2220000000002-22-200000000000000002i−2i−2i2i000000002i−2i0000000
χ462-2-222-22-22-222-2-2-22-222-22-22-2000000-2-2220000000002-22-20000000000000000−2i2i2i−2i00000000−2i2i0000000
χ472-2-222-22-22-222-2-2-22-222-2-22-22000000-2-222000000000-22-2200000000000000002i−2i−2i2i00000000−2i2i0000000
χ482-2-222-22-22-222-2-2-22-222-2-22-22000000-2-222000000000-22-220000000000000000−2i2i2i−2i000000002i−2i0000000
χ492-2-22-22-222-22-22-2-2-22-2222-2-22000000-222-20000000002-2-220000000000000000000000000000002-2002-20
χ502-2-22-22-222-22-22-2-2-22-2222-2-22000000-222-20000000002-2-22000000000000000000000000000000-2200-220
χ512-2-22-22-222-22-22-2-2-22-222-222-2000000-222-2000000000-222-20000000000000000000000000000002-200-220
χ522-2-22-22-222-22-22-2-2-22-222-222-2000000-222-2000000000-222-2000000000000000000000000000000-22002-20
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
χ554444-4-4-4-44-4-44444-4-4-44-40000000000-44-4400000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-444-2-2222-220000002323−23−232-22-20000000000000−232300000000000000000000000000000000000
χ574444-4-4-4-4-2-4-444-2-2222-22000000−23−2323232-22-2000000000000023−2300000000000000000000000000000000000
χ5844-4-444-4-4400004-44-4-4-4400000000000000000000022−220000000000000022−2222−2200000000000000000000000
χ5944-4-444-4-4400004-44-4-4-44000000000000000000000−222200000000000000−2222−222200000000000000000000000
χ6044-4-444-4-4-20000-22-2222-200000023−2323−230000000000022−2200000000006−66−6−22−2200000000000000000000000
χ6144-4-444-4-4-20000-22-2222-200000023−2323−2300000000000−22220000000000−66−662−22−200000000000000000000000
χ6244-4-444-4-4-20000-22-2222-2000000−2323−23230000000000022−220000000000−66−66−22−2200000000000000000000000
χ6344-4-444-4-4-20000-22-2222-2000000−2323−232300000000000−222200000000006−66−62−22−200000000000000000000000
χ6444-4-4-4-444400004-4-444-4-400004-44-4-44000000000000000000000000000000000000000000000000000000
χ6544-4-4-4-444400004-4-444-4-40000-44-444-4000000000000000000000000000000000000000000000000000000
χ6644-4-4-4-444-20000-222-2-22200004-4-222-2000000000000000000000006−6−66−666−600000000000000000000000
χ6744-4-4-4-444-20000-222-2-22200004-4-222-200000000000000000000000−666−66−6−6600000000000000000000000
χ6844-4-4-4-444-20000-222-2-2220000-442-2-22000000000000000000000006−6−666−6−6600000000000000000000000
χ6944-4-4-4-444-20000-222-2-2220000-442-2-2200000000000000000000000−666−6−666−600000000000000000000000
χ704-44-44-4-4440000-4444-4-4-400000000000000000000000000000000000000000000000000000000000−2i22i2000
χ714-44-44-4-4440000-4444-4-4-4000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ724-44-4-444-440000-44-4-44-44000000000000000000000000000000000000000004i−4i000000000000000000000
χ734-44-4-444-440000-44-4-44-4400000000000000000000000000000000000000000−4i4i000000000000000000000
χ744-4-444-44-4-24-4-4422-22-2-220000000000-2-2220004i−4i0000000000−2i2i−2i2i0000000000000000000000000000000
χ754-4-444-44-4-24-4-4422-22-2-220000000000-2-222000−4i4i00000000002i−2i2i−2i0000000000000000000000000000000
χ764-4-444-44-4-2-444-422-22-2-224-44-400000022-2-2000000000-22-220000000000000000000000000000000000000
χ774-4-444-44-4-2-444-422-22-2-22-44-4400000022-2-20000000002-22-20000000000000000000000000000000000000
χ784-4-44-44-4444-44-4-4-4-44-44400000000004-4-4400000000000000000000000000000000000000000000000000
χ794-4-44-44-44-24-44-4222-22-2-20000000000-222-2000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ804-4-44-44-44-24-44-4222-22-2-20000000000-222-20000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ814-4-44-44-44-2-44-44222-22-2-24-4-440000002-2-22000000000-222-20000000000000000000000000000000000000
χ824-4-44-44-44-2-44-44222-22-2-2-444-40000002-2-220000000002-2-220000000000000000000000000000000000000
χ838-88-88-8-88-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-888-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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