Finite Group Databasebeta

← Group #10835930

Character table — Group #10835930

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order1222222234444666666644448888888812121212121212121212121224242424242424242424242424242424444444442466121212121212244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11-1-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-111-1111111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111111-11111-1-1-1-1-111-1-1-111-1-1-11
χ1011111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-1-1-11-1-1111-1-1111-1
χ1111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-11111-1-1-1-11111-1-11-1
χ1211111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-111111111-1-1-1-111-11
χ1311111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-11-1-11111-1-1-111-1-1-1-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-1-11111-1-11-1-111111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111111-111-1-1-1-111-1-1-1-111-1-111-11
χ1611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-111-1-1-1-1111111-1-111-1-11-1
χ17222222222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-2-2-20000000000000000000022-2-20000000000-200200000000
χ18222222222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-2-2-200000000000000000000-2-2220000000000200-200000000
χ19222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-22222-2-20000000000000000000022-2-20000000000200-200000000
χ20222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-22222-2-200000000000000000000-2-2220000000000-200200000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122220000-2-211-1-111-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-2000022-1-111-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-200002-2-1-1-1-11111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-2220000-221111-1-1-1-1000000000000
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
χ2922-22-2-2-2222-22-22-22-22-2-22i−2i2i−2i000000002-22i2i−2i−2i2i2i−2i−2i2-200000000000000002-22i−2i000000002-2002i−2i000000000000
χ3022-22-2-2-2222-22-22-22-22-2-22i−2i2i−2i000000002-22i2i−2i−2i2i2i−2i−2i2-20000000000000000-22−2i2i00000000-2200−2i2i000000000000
χ3122-22-2-2-2222-22-22-22-22-2-2−2i2i−2i2i000000002-2−2i−2i2i2i−2i−2i2i2i2-200000000000000002-2−2i2i000000002-200−2i2i000000000000
χ3222-22-2-2-2222-22-22-22-22-2-2−2i2i−2i2i000000002-2−2i−2i2i2i−2i−2i2i2i2-20000000000000000-222i−2i00000000-22002i−2i000000000000
χ3322-22-2-2-222-22-222-22-22-2-22i−2i−2i2i00000000-222i2i−2i−2i−2i−2i2i2i-22000000000000000000000000000000000002i−2i02-2000000
χ3422-22-2-2-222-22-222-22-22-2-22i−2i−2i2i00000000-222i2i−2i−2i−2i−2i2i2i-2200000000000000000000000000000000000−2i2i0-22000000
χ3522-22-2-2-222-22-222-22-22-2-2−2i2i2i−2i00000000-22−2i−2i2i2i2i2i−2i−2i-22000000000000000000000000000000000002i−2i0-22000000
χ3622-22-2-2-222-22-222-22-22-2-2−2i2i2i−2i00000000-22−2i−2i2i2i2i2i−2i−2i-2200000000000000000000000000000000000−2i2i02-2000000
χ3722-22-2-2-22-12-22-2-11-11-1112i−2i2i−2i00000000-11−i−iii−i−iii-11−i3−i3−i3−i3i3i3i3i33333−3−3−3−32-22i−2i000000−i3i3-113−3−ii000000000000
χ3822-22-2-2-22-12-22-2-11-11-1112i−2i2i−2i00000000-11−i−iii−i−iii-11−i3−i3−i3−i3i3i3i3i33333−3−3−3−3-22−2i2i000000i3−i31-1−33i−i000000000000
χ3922-22-2-2-22-12-22-2-11-11-1112i−2i2i−2i00000000-11−i−iii−i−iii-11i3i3i3i3−i3−i3−i3−i3−3−3−3−333332-22i−2i000000i3−i3-11−33−ii000000000000
χ4022-22-2-2-22-12-22-2-11-11-1112i−2i2i−2i00000000-11−i−iii−i−iii-11i3i3i3i3−i3−i3−i3−i3−3−3−3−33333-22−2i2i000000−i3i31-13−3i−i000000000000
χ4122-22-2-2-22-12-22-2-11-11-111−2i2i−2i2i00000000-11ii−i−iii−i−i-11−i3−i3−i3−i3i3i3i3i3−3−3−3−333332-2−2i2i000000−i3i3-11−33i−i000000000000
χ4222-22-2-2-22-12-22-2-11-11-111−2i2i−2i2i00000000-11ii−i−iii−i−i-11−i3−i3−i3−i3i3i3i3i3−3−3−3−33333-222i−2i000000i3−i31-13−3−ii000000000000
χ4322-22-2-2-22-12-22-2-11-11-111−2i2i−2i2i00000000-11ii−i−iii−i−i-11i3i3i3i3−i3−i3−i3−i33333−3−3−3−32-2−2i2i000000i3−i3-113−3i−i000000000000
χ4422-22-2-2-22-12-22-2-11-11-111−2i2i−2i2i00000000-11ii−i−iii−i−i-11i3i3i3i3−i3−i3−i3−i33333−3−3−3−3-222i−2i000000−i3i31-1−33−ii000000000000
χ452-2-2-222-22222-2-2-2-222-2-2200002i2i−2i−2i00002200000000-2-22i2i−2i−2i2i2i−2i−2i0000000000002-22-200000000000000002i−2i0000
χ462-2-2-222-22222-2-2-2-222-2-2200002i2i−2i−2i00002200000000-2-22i2i−2i−2i2i2i−2i−2i000000000000-22-220000000000000000−2i2i0000
χ472-2-2-222-22222-2-2-2-222-2-220000−2i−2i2i2i00002200000000-2-2−2i−2i2i2i−2i−2i2i2i0000000000002-22-20000000000000000−2i2i0000
χ482-2-2-222-22222-2-2-2-222-2-220000−2i−2i2i2i00002200000000-2-2−2i−2i2i2i−2i−2i2i2i000000000000-22-2200000000000000002i−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
χ55444-4-44-4-44000044-4-4-4-440000000022−2222−220000000000000000000022−2222−2222−2222−22000000000000000000000000000000
χ56444-4-44-4-44000044-4-4-4-4400000000−2222−222200000000000000000000−2222−2222−2222−2222000000000000000000000000000000
χ57444-4-44-4-4-20000-2-22222-20000000022−2222−220023−2323−230000006−66−66−66−6−22−22−22−22000000000000000000000000000000
χ58444-4-44-4-4-20000-2-22222-20000000022−2222−2200−2323−2323000000−66−66−66−66−22−22−22−22000000000000000000000000000000
χ59444-4-44-4-4-20000-2-22222-200000000−2222−22220023−2323−23000000−66−66−66−662−22−22−22−2000000000000000000000000000000
χ60444-4-44-4-4-20000-2-22222-200000000−2222−222200−2323−23230000006−66−66−66−62−22−22−22−2000000000000000000000000000000
χ6144-44-4-4-44-2-44-44-22-22-2224i−4i−4i4i000000002-2−2i−2i2i2i2i2i−2i−2i2-20000000000000000000000000000000000000000000000
χ6244-44-4-4-44-2-44-44-22-22-222−4i4i4i−4i000000002-22i2i−2i−2i−2i−2i2i2i2-20000000000000000000000000000000000000000000000
χ6344-4-44-44-4400004-4-44-44-40000−2i22i2−2i22i20000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ6444-4-44-44-4400004-4-44-44-400002i2−2i22i2−2i200000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ6544-4-44-44-4-20000-222-22-220000−2i22i2−2i22i2000000−2i32i32i3−2i3000000i2−i2i2−i2−i2i2−i2i26−66−6−66−66000000000000000000000000000000
χ6644-4-44-44-4-20000-222-22-220000−2i22i2−2i22i20000002i3−2i3−2i32i3000000i2−i2i2−i2−i2i2−i2i2−66−666−66−6000000000000000000000000000000
χ6744-4-44-44-4-20000-222-22-2200002i2−2i22i2−2i2000000−2i32i32i3−2i3000000−i2i2−i2i2i2−i2i2−i2−66−666−66−6000000000000000000000000000000
χ6844-4-44-44-4-20000-222-22-2200002i2−2i22i2−2i20000002i3−2i3−2i32i3000000−i2i2−i2i2i2−i2i2−i26−66−6−66−66000000000000000000000000000000
χ694-4444-4-4-440000-44-444-4-4000022−22−2222000000000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ704-4444-4-4-440000-44-444-4-40000−222222−220000000000000000−222222−2222−22−222200000000000000000000000000000000000000
χ714-4444-4-4-4-200002-22-2-222000022−22−2222000000000023−2323−2300−222−22−2−226−6−66−666−6000000000000000000000000000000
χ724-4444-4-4-4-200002-22-2-222000022−22−22220000000000−2323−232300−222−22−2−22−666−66−6−66000000000000000000000000000000
χ734-4444-4-4-4-200002-22-2-2220000−222222−22000000000023−2323−23002−2−22−222−2−666−66−6−66000000000000000000000000000000
χ744-4444-4-4-4-200002-22-2-2220000−222222−220000000000−2323−2323002−2−22−222−26−6−66−666−6000000000000000000000000000000
χ754-44-4-4-44444-4-44-444-4-44-40000000000004-400000000-440000000000000000000000000000000000000000000000
χ764-44-4-4-4444-444-4-444-4-44-4000000000000-44000000004-40000000000000000000000000000000000000000000000
χ774-44-4-4-444-24-4-442-2-222-22000000000000-22000000002-22323−23−23−23−23232300000000000000000000000000000000000000
χ784-44-4-4-444-24-4-442-2-222-22000000000000-22000000002-2−23−2323232323−23−2300000000000000000000000000000000000000
χ794-44-4-4-444-2-444-42-2-222-220000000000002-200000000-22000000002323−23−23−23−232323000000000000000000000000000000
χ804-44-4-4-444-2-444-42-2-222-220000000000002-200000000-2200000000−23−2323232323−23−23000000000000000000000000000000
χ814-4-44-444-440000-4-4-4-44440000000022−22−22220000000000000000000022−22−222222−22−2222000000000000000000000000000000
χ824-4-44-444-440000-4-4-4-444400000000−222222−2200000000000000000000−222222−22−222222−22000000000000000000000000000000
χ834-4-44-444-4-200002222-2-2-20000000022−22−2222000000−2i32i32i3−2i300−i6i6i6−i6−i6i6i6−i6−222−2−222−2000000000000000000000000000000
χ844-4-44-444-4-200002222-2-2-20000000022−22−22220000002i3−2i3−2i32i300i6−i6−i6i6i6−i6−i6i6−222−2−222−2000000000000000000000000000000
χ854-4-44-444-4-200002222-2-2-200000000−222222−22000000−2i32i32i3−2i300i6−i6−i6i6i6−i6−i6i62−2−222−2−22000000000000000000000000000000
χ864-4-44-444-4-200002222-2-2-200000000−222222−220000002i3−2i3−2i32i300−i6i6i6−i6−i6i6i6−i62−2−222−2−22000000000000000000000000000000
χ874-4-4-444-44-244-4-422-2-222-200004i4i−4i−4i0000-2-20000000022−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000
χ884-4-4-444-44-244-4-422-2-222-20000−4i−4i4i4i0000-2-200000000222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000
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).