Finite Group Databasebeta

← Group #10844910

Character table — Group #10844910

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order1222222234444666666644448888888812121212121212121212121224242424242424242424242424242424444444442466121212121212224444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-11111-1-1-1-1-1-11111-1-1-1-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-1-1-111-1-1-1-11111-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-1111111-1-111-1-1-1-1-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-11111-1-111-1-111111-1
χ911111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-111-1-1-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111
χ1111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-11-1-11111-1-1-1-111-1-1-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-1-11111-1-111-1-11111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111111-111-1-1-1-11111-1-1-1-1-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-111-1-1-1-111-1-1111111-1-1-11
χ17222222222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-2-2-20000000000000000000022-2-200000000000000-22000000
χ18222222222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-2-2-200000000000000000000-2-222000000000000002-2000000
χ19222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-22222-2-20000000000000000000022-2-2000000000000002-2000000
χ20222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-22222-2-200000000000000000000-2-22200000000000000-22000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-200002-2-1-1-1-11111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2220000-221111-1-1-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122220000-2-211-1-111-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2000022-1-111-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-122-2-20000-2211-1-1-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1-2-22200002-2-1-11111-1-1000000000000
χ29222-22-2-2-222-2-222-22-22-2-200002i2i−2i−2i00002-2000000002-22i2i2i2i−2i−2i−2i−2i000000000000000000000000002-22i−2i00000000
χ30222-22-2-2-222-2-222-22-22-2-200002i2i−2i−2i00002-2000000002-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000-22−2i2i00000000
χ31222-22-2-2-222-2-222-22-22-2-20000−2i−2i2i2i00002-2000000002-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000002-2−2i2i00000000
χ32222-22-2-2-222-2-222-22-22-2-20000−2i−2i2i2i00002-2000000002-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000-222i−2i00000000
χ332-2-222-22-222-22-2-222-2-22-200002-22-200002-200000000-2222-2-222-2-2000000002i−2i2i−2i000000002i−2i002i−2i000000000000
χ342-2-222-22-222-22-2-222-2-22-200002-22-200002-200000000-2222-2-222-2-200000000−2i2i−2i2i00000000−2i2i00−2i2i000000000000
χ352-2-222-22-222-22-2-222-2-22-20000-22-2200002-200000000-22-2-222-2-222000000002i−2i−2i2i000000002i−2i00−2i2i000000000000
χ362-2-222-22-222-22-2-222-2-22-20000-22-2200002-200000000-22-2-222-2-22200000000−2i2i2i−2i00000000−2i2i002i−2i000000000000
χ372-2-222-22-2-12-22-21-1-111-1100002-22-20000-1133−3−333−3−31-1-1-111-1-1113333−3−3−3−32i−2i2i−2i000000−i3i3−ii−i3i3−ii000000000000
χ382-2-222-22-2-12-22-21-1-111-1100002-22-20000-1133−3−333−3−31-1-1-111-1-1113333−3−3−3−3−2i2i−2i2i000000i3−i3i−ii3−i3i−i000000000000
χ392-2-222-22-2-12-22-21-1-111-1100002-22-20000-11−3−333−3−3331-1-1-111-1-111−3−3−3−333332i−2i2i−2i000000i3−i3−iii3−i3−ii000000000000
χ402-2-222-22-2-12-22-21-1-111-1100002-22-20000-11−3−333−3−3331-1-1-111-1-111−3−3−3−33333−2i2i−2i2i000000−i3i3i−i−i3i3i−i000000000000
χ412-2-222-22-2-12-22-21-1-111-110000-22-220000-1133−3−333−3−31-111-1-111-1-1−3−3−3−333332i−2i−2i2i000000−i3i3−iii3−i3i−i000000000000
χ422-2-222-22-2-12-22-21-1-111-110000-22-220000-1133−3−333−3−31-111-1-111-1-1−3−3−3−33333−2i2i2i−2i000000i3−i3i−i−i3i3−ii000000000000
χ432-2-222-22-2-12-22-21-1-111-110000-22-220000-11−3−333−3−3331-111-1-111-1-13333−3−3−3−32i−2i−2i2i000000i3−i3−ii−i3i3i−i000000000000
χ442-2-222-22-2-12-22-21-1-111-110000-22-220000-11−3−333−3−3331-111-1-111-1-13333−3−3−3−3−2i2i2i−2i000000−i3i3i−ii3−i3−ii000000000000
χ452-2-2-222-22222-2-2-2-222-2-2200002i−2i−2i2i00002200000000-2-22i2i−2i−2i−2i−2i2i2i0000000000002-22-200000000000000002i−2i0000
χ462-2-2-222-22222-2-2-2-222-2-2200002i−2i−2i2i00002200000000-2-22i2i−2i−2i−2i−2i2i2i000000000000-22-220000000000000000−2i2i0000
χ472-2-2-222-22222-2-2-2-222-2-220000−2i2i2i−2i00002200000000-2-2−2i−2i2i2i2i2i−2i−2i0000000000002-22-20000000000000000−2i2i0000
χ482-2-2-222-22222-2-2-2-222-2-220000−2i2i2i−2i00002200000000-2-2−2i−2i2i2i2i2i−2i−2i000000000000-22-2200000000000000002i−2i0000
χ492-2-2-222-222-2-222-2-222-2-220000000022-2-2-2-200000000220000000022-2-222-2-200002-2-220000000000000000002-200
χ502-2-2-222-222-2-222-2-222-2-220000000022-2-2-2-200000000220000000022-2-222-2-20000-222-2000000000000000000-2200
χ512-2-2-222-222-2-222-2-222-2-2200000000-2-222-2-2000000002200000000-2-222-2-22200002-2-22000000000000000000-2200
χ522-2-2-222-222-2-222-2-222-2-2200000000-2-222-2-2000000002200000000-2-222-2-2220000-222-20000000000000000002-200
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000000022-2-2-2-22222220000000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44400000000222222-2-2-2-2220000000000000000000000000000000000000000000000
χ55444-44-4-4-44-444-44-44-44-4-4000000000000-4400000000-440000000000000000000000000000000000000000000000
χ56444-44-4-4-4-24-4-44-22-22-22200004i4i−4i−4i0000-2200000000-22−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000
χ57444-44-4-4-4-24-4-44-22-22-2220000−4i−4i4i4i0000-2200000000-222i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000
χ58444-44-4-4-4-2-444-4-22-22-2220000000000002-2000000002-2000000002323−23−23−23−232323000000000000000000000000000000
χ59444-44-4-4-4-2-444-4-22-22-2220000000000002-2000000002-200000000−23−2323232323−23−23000000000000000000000000000000
χ6044-44-4-4-444000044-4-4-4-444i−4i0000000000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ6144-44-4-4-444000044-4-4-4-44−4i4i000000000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ6244-44-4-4-44-20000-2-22222-24i−4i000000000000−2i2i−2i2i0000006−66−66−66−6i6−i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ6344-44-4-4-44-20000-2-22222-24i−4i000000000000−2i2i−2i2i000000−66−66−66−66−i6i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ6444-44-4-4-44-20000-2-22222-2−4i4i0000000000002i−2i2i−2i0000006−66−66−66−6−i6i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ6544-44-4-4-44-20000-2-22222-2−4i4i0000000000002i−2i2i−2i000000−66−66−66−66i6−i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ6644-4-4-444-4400004-4-44-44-400000000−2i22i2−2i22i200000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ6744-4-4-444-4400004-4-44-44-4000000002i2−2i22i2−2i2000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ6844-4-4-444-4-20000-222-22-2200000000−2i22i2−2i22i200000023−2323−2300i6−i6i6−i6−i6i6−i6i6i2−i2−i2i2−i2i2i2−i2000000000000000000000000000000
χ6944-4-4-444-4-20000-222-22-2200000000−2i22i2−2i22i2000000−2323−232300−i6i6−i6i6i6−i6i6−i6i2−i2−i2i2−i2i2i2−i2000000000000000000000000000000
χ7044-4-4-444-4-20000-222-22-22000000002i2−2i22i2−2i200000023−2323−2300−i6i6−i6i6i6−i6i6−i6−i2i2i2−i2i2−i2−i2i2000000000000000000000000000000
χ7144-4-4-444-4-20000-222-22-22000000002i2−2i22i2−2i2000000−2323−232300i6−i6i6−i6−i6i6−i6i6−i2i2i2−i2i2−i2−i2i2000000000000000000000000000000
χ724-444-44-4-440000-44-444-4-400000000−2i22i22i2−2i200000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ734-444-44-4-440000-44-444-4-4000000002i2−2i2−2i22i2000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ744-444-44-4-4-200002-22-2-22200000000−2i22i22i2−2i200−2i32i32i3−2i3000000−666−6−666−6i2−i2i2−i2−i2i2−i2i2000000000000000000000000000000
χ754-444-44-4-4-200002-22-2-22200000000−2i22i22i2−2i2002i3−2i3−2i32i30000006−6−666−6−66i2−i2i2−i2−i2i2−i2i2000000000000000000000000000000
χ764-444-44-4-4-200002-22-2-222000000002i2−2i2−2i22i200−2i32i32i3−2i30000006−6−666−6−66−i2i2−i2i2i2−i2i2−i2000000000000000000000000000000
χ774-444-44-4-4-200002-22-2-222000000002i2−2i2−2i22i2002i3−2i3−2i32i3000000−666−6−666−6−i2i2−i2i2i2−i2i2−i2000000000000000000000000000000
χ784-44-4-4-44440000-4-4-4-4444004-4000000000000004-4-44000000000000000000000000000000000000000000000000
χ794-44-4-4-44440000-4-4-4-444400-4400000000000000-444-4000000000000000000000000000000000000000000000000
χ804-44-4-4-444-200002222-2-2-2004-400000000000000-222-200i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000
χ814-44-4-4-444-200002222-2-2-2004-400000000000000-222-200−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000
χ824-44-4-4-444-200002222-2-2-200-44000000000000002-2-2200i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000
χ834-44-4-4-444-200002222-2-2-200-44000000000000002-2-2200−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000
χ844-4-444-44-44-44-44-444-4-44-4000000000000-44000000004-40000000000000000000000000000000000000000000000
χ854-4-444-44-4-2-44-442-2-222-220000000000002-22323−23−23−23−232323-220000000000000000000000000000000000000000000000
χ864-4-444-44-4-2-44-442-2-222-220000000000002-2−23−2323232323−23−23-220000000000000000000000000000000000000000000000
χ874-4-4-444-44-244-4-422-2-222-200004i−4i−4i4i0000-2-20000000022−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000
χ884-4-4-444-44-244-4-422-2-222-20000−4i4i4i−4i0000-2-200000000222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000
χ894-4-4-444-44-2-4-44422-2-222-20000000044-4-42200000000-2-200000000-2-222-2-222000000000000000000000000000000
χ904-4-4-444-44-2-4-44422-2-222-200000000-4-4442200000000-2-20000000022-2-222-2-2000000000000000000000000000000

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