Finite Group Databasebeta

← Group #10845518

Character table — Group #10845518

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order122222223444466666662244666688888888121212121212121224242424242424242424242424242424224444444466121212121212244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-11111-1-1-1-111-1-111-1-1-1-11-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-1-1-1-1-111-1-11111-11
χ71111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-111111111-1-1-1-1-1-1-11
χ81111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-11111111-1
χ911111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1111111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-11111-1111-1-1-1-111-1-1-1-111-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1111-1-1-1-1111111-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111111-1-1-11111-1-1-1-111-1-1-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-1-11111-1-111-1-11111-1-1-11
χ17222222222-2-2-2-2222222222-2-2222200000000-2-2-2-2-2-2-2-20000000000000000000022-2-20000000000-220000000000
χ18222222222-2-2-2-2222222222-2-2222200000000-2-2-2-2-2-2-2-200000000000000000000-2-22200000000002-20000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-200000000-2-2-22222-20000000000000000000022-2-200000000002-20000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-200000000-2-2-22222-200000000000000000000-2-2220000000000-220000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-200002-2-1-1-1-11111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2220000-221111-1-1-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111122220000-2-2-1-111-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111-2-2-2-200002211-1-111-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-122-2-20000-22-1-11111-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-1-2-22200002-211-1-1-1-111000000000000
χ292222-2-2-2-222-2-222-2-222-2-20000000022-2-200002-2-2000022222-2-2-2-200000000000000000000000000002i−2i2i−2i000000
χ302222-2-2-2-222-2-222-2-222-2-20000000022-2-200002-2-2000022222-2-2-2-20000000000000000000000000000−2i2i−2i2i000000
χ312222-2-2-2-222-2-222-2-222-2-200000000-2-22200002-2-200002-2-2-2-2222200000000000000000000000000002i−2i−2i2i000000
χ322222-2-2-2-222-2-222-2-222-2-200000000-2-22200002-2-200002-2-2-2-222220000000000000000000000000000−2i2i2i−2i000000
χ332-2-2222-2-222-22-2-22-22-22-2000000002i−2i2i−2i000022-20000-22i2i−2i−2i2i2i−2i−2i000000002-22i−2i0000002-2002i−2i00000000000000
χ342-2-2222-2-222-22-2-22-22-22-2000000002i−2i2i−2i000022-20000-22i2i−2i−2i2i2i−2i−2i00000000-22−2i2i000000-2200−2i2i00000000000000
χ352-2-2222-2-222-22-2-22-22-22-200000000−2i2i−2i2i000022-20000-2−2i−2i2i2i−2i−2i2i2i000000002-2−2i2i0000002-200−2i2i00000000000000
χ362-2-2222-2-222-22-2-22-22-22-200000000−2i2i−2i2i000022-20000-2−2i−2i2i2i−2i−2i2i2i00000000-222i−2i000000-22002i−2i00000000000000
χ372-2-2222-2-2-12-22-21-11-11-110000−i3−i3i3i32i−2i2i−2i0000-1-11−i3−i3i3i31−i−iii−i−iii3333−3−3−3−32-22i−2i000000-11−i3i3−ii3−3000000000000
χ382-2-2222-2-2-12-22-21-11-11-110000−i3−i3i3i32i−2i2i−2i0000-1-11−i3−i3i3i31−i−iii−i−iii3333−3−3−3−3-22−2i2i0000001-1i3−i3i−i−33000000000000
χ392-2-2222-2-2-12-22-21-11-11-110000−i3−i3i3i3−2i2i−2i2i0000-1-11−i3−i3i3i31ii−i−iii−i−i−3−3−3−333332-2−2i2i000000-11−i3i3i−i−33000000000000
χ402-2-2222-2-2-12-22-21-11-11-110000−i3−i3i3i3−2i2i−2i2i0000-1-11−i3−i3i3i31ii−i−iii−i−i−3−3−3−33333-222i−2i0000001-1i3−i3−ii3−3000000000000
χ412-2-2222-2-2-12-22-21-11-11-110000i3i3−i3−i32i−2i2i−2i0000-1-11i3i3−i3−i31−i−iii−i−iii−3−3−3−333332-22i−2i000000-11i3−i3−ii−33000000000000
χ422-2-2222-2-2-12-22-21-11-11-110000i3i3−i3−i32i−2i2i−2i0000-1-11i3i3−i3−i31−i−iii−i−iii−3−3−3−33333-22−2i2i0000001-1−i3i3i−i3−3000000000000
χ432-2-2222-2-2-12-22-21-11-11-110000i3i3−i3−i3−2i2i−2i2i0000-1-11i3i3−i3−i31ii−i−iii−i−i3333−3−3−3−32-2−2i2i000000-11i3−i3i−i3−3000000000000
χ442-2-2222-2-2-12-22-21-11-11-110000i3i3−i3−i3−2i2i−2i2i0000-1-11i3i3−i3−i31ii−i−iii−i−i3333−3−3−3−3-222i−2i0000001-1−i3i3−ii−33000000000000
χ452-2-22-2-222222-2-2-2-222-2-22000000002i−2i−2i2i00002-220000-22i2i−2i−2i−2i−2i2i2i0000000000002-22-200000000000000002i−2i0000
χ462-2-22-2-222222-2-2-2-222-2-22000000002i−2i−2i2i00002-220000-22i2i−2i−2i−2i−2i2i2i000000000000-22-220000000000000000−2i2i0000
χ472-2-22-2-222222-2-2-2-222-2-2200000000−2i2i2i−2i00002-220000-2−2i−2i2i2i2i2i−2i−2i0000000000002-22-20000000000000000−2i2i0000
χ482-2-22-2-222222-2-2-2-222-2-2200000000−2i2i2i−2i00002-220000-2−2i−2i2i2i2i2i−2i−2i000000000000-22-2200000000000000002i−2i0000
χ492-2-22-2-2222-2-222-2-222-2-2200000000000022-2-2-22-2000020000000022-2-222-2-200002-2-220000000000000000002-200
χ502-2-22-2-2222-2-222-2-222-2-2200000000000022-2-2-22-2000020000000022-2-222-2-20000-222-2000000000000000000-2200
χ512-2-22-2-2222-2-222-2-222-2-22000000000000-2-222-22-20000200000000-2-222-2-22200002-2-22000000000000000000-2200
χ522-2-22-2-2222-2-222-2-222-2-22000000000000-2-222-22-20000200000000-2-222-2-2220000-222-20000000000000000002-200
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-200000000222222220000000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222200000000222-2-2-2-220000000000000000000000000000000000000000000000
χ554444-4-4-4-44-444-44-4-444-4-40000000000000000-4440000-40000000000000000000000000000000000000000000000
χ564444-4-4-4-4-24-4-44-222-2-2220000000044-4-40000-2220000-2-2-2-2-2222200000000000000000000000000000000000000
χ574444-4-4-4-4-24-4-44-222-2-22200000000-4-4440000-2220000-22222-2-2-2-200000000000000000000000000000000000000
χ584444-4-4-4-4-2-444-4-222-2-22200000000000000002-2-200002000000002323−23−23−23−232323000000000000000000000000000000
χ594444-4-4-4-4-2-444-4-222-2-22200000000000000002-2-20000200000000−23−2323232323−23−23000000000000000000000000000000
χ6044-4-44-4-444000044-4-4-4-44004i−4i0000000000000004i−4i4i−4i00000000000000000000000000000000000000000000000
χ6144-4-44-4-444000044-4-4-4-4400−4i4i000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000
χ6244-4-44-4-44-20000-2-22222-2004i−4i000000000000000−2i2i−2i2i06−66−66−66−6i6−i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ6344-4-44-4-44-20000-2-22222-2004i−4i000000000000000−2i2i−2i2i0−66−66−66−66−i6i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ6444-4-44-4-44-20000-2-22222-200−4i4i0000000000000002i−2i2i−2i06−66−66−66−6−i6i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ6544-4-44-4-44-20000-2-22222-200−4i4i0000000000000002i−2i2i−2i0−66−66−66−66i6−i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ6644-4-4-444-4400004-44-4-44-4000000000000−2i22i2−2i22i20000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ6744-4-4-444-4400004-44-4-44-40000000000002i2−2i22i2−2i200000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ6844-4-4-444-4-20000-22-222-220000−2i32i3−2i32i30000−2i22i2−2i22i2000000006−66−6−66−66i2−i2−i2i2−i2i2i2−i2000000000000000000000000000000
χ6944-4-4-444-4-20000-22-222-220000−2i32i3−2i32i300002i2−2i22i2−2i200000000−66−666−66−6−i2i2i2−i2i2−i2−i2i2000000000000000000000000000000
χ7044-4-4-444-4-20000-22-222-2200002i3−2i32i3−2i30000−2i22i2−2i22i200000000−66−666−66−6i2−i2−i2i2−i2i2i2−i2000000000000000000000000000000
χ7144-4-4-444-4-20000-22-222-2200002i3−2i32i3−2i300002i2−2i22i2−2i2000000006−66−6−66−66−i2i2i2−i2i2−i2−i2i2000000000000000000000000000000
χ724-44-44-44-440000-444-44-4-4000000000000−2i22i22i2−2i20000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ734-44-44-44-440000-444-44-4-40000000000002i2−2i2−2i22i200000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ744-44-44-44-4-200002-2-22-222000000000000−2i22i22i2−2i200023−23−23230i6−i6−i6i6i6−i6−i6i6i2−i2i2−i2−i2i2−i2i2000000000000000000000000000000
χ754-44-44-44-4-200002-2-22-222000000000000−2i22i22i2−2i2000−232323−230−i6i6i6−i6−i6i6i6−i6i2−i2i2−i2−i2i2−i2i2000000000000000000000000000000
χ764-44-44-44-4-200002-2-22-2220000000000002i2−2i2−2i22i200023−23−23230−i6i6i6−i6−i6i6i6−i6−i2i2−i2i2i2−i2i2−i2000000000000000000000000000000
χ774-44-44-44-4-200002-2-22-2220000000000002i2−2i2−2i22i2000−232323−230i6−i6−i6i6i6−i6−i6i6−i2i2−i2i2i2−i2i2−i2000000000000000000000000000000
χ784-44-4-44-4440000-4-4-4-44444-4004-4-4400000000000000000000000000000000000000000000000000000000000000
χ794-44-4-44-4440000-4-4-4-4444-4400-444-400000000000000000000000000000000000000000000000000000000000000
χ804-44-4-44-44-200002222-2-2-24-400-222-20000000000000000i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000
χ814-44-4-44-44-200002222-2-2-24-400-222-20000000000000000−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000
χ824-44-4-44-44-200002222-2-2-2-44002-2-220000000000000000i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000
χ834-44-4-44-44-200002222-2-2-2-44002-2-220000000000000000−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000
χ844-4-4444-4-44-44-44-44-44-44-40000000000000000-4-44000040000000000000000000000000000000000000000000000
χ854-4-4444-4-4-2-44-442-22-22-220000−2i3−2i32i32i30000000022-22i32i3−2i3−2i3-20000000000000000000000000000000000000000000000
χ864-4-4444-4-4-2-44-442-22-22-2200002i32i3−2i3−2i30000000022-2−2i3−2i32i32i3-20000000000000000000000000000000000000000000000
χ874-4-44-4-444-244-4-422-2-222-2000000004i−4i−4i4i0000-22-200002−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000
χ884-4-44-4-444-244-4-422-2-222-200000000−4i4i4i−4i0000-22-2000022i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000
χ894-4-44-4-444-2-4-44422-2-222-200000000000044-4-42-220000-200000000-2-222-2-222000000000000000000000000000000
χ904-4-44-4-444-2-4-44422-2-222-2000000000000-4-4442-220000-20000000022-2-222-2-2000000000000000000000000000000

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