Finite Group Databasebeta

← Group #10835913

Character table — Group #10835913

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order122222223444466666664444888888881212121212121212121212122424242424242424242424242424242444444444441212121212121212244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111-1-1-1-11-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-11111-11111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111111-11111-1-1-1-1-111-1-1-111-1-11-1
χ1011111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-1-1-11-1-1111-1-111-11
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-11111-1-1-111-111-1-1-11
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-11111111-1-11-1-1111-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1111-1-1-1-111-111-1-1-1-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1111-1-1-1-1111-1-111111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111111-1-1-11111-1-1-1-1-111-1-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-1-11111-1-1111-1-1111-1-1-11
χ17222222222-2-2-2-2222222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000022-2-20000000000-200002000000
χ18222222222-2-2-2-2222222222-2-2000000002222-2-2-2-2-2-2-2-200000000000000000000-2-222000000000020000-2000000
χ19222222222-2-2-2-22222222-2-22200000000-2-2-2-22222-2-2-2-20000000000000000000022-2-2000000000020000-2000000
χ20222222222-2-2-2-22222222-2-22200000000-2-2-2-22222-2-2-2-200000000000000000000-2-2220000000000-200002000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122220000-2-2-1-111-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-200002211-1-111-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-200002-2-1-1-1-11111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2220000-221111-1-1-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-122-2-20000-22-1-11111-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-1-2-22200002-211-1-1-1-111000000000000
χ2922-2-22-2-2222-22-222-2-2-2-222i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i2-22-200000000000000002i−2i2-20000002i−2i002-200000000000000
χ3022-2-22-2-2222-22-222-2-2-2-222i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i2-22-20000000000000000−2i2i-22000000−2i2i00-2200000000000000
χ3122-2-22-2-2222-22-222-2-2-2-22−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i2-22-200000000000000002i−2i-220000002i−2i00-2200000000000000
χ3222-2-22-2-2222-22-222-2-2-2-22−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i2-22-20000000000000000−2i2i2-2000000−2i2i002-200000000000000
χ3322-2-22-2-222-22-2222-2-2-2-222i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i-22-22000000000000000000000000000000000002-22i−2i0000000
χ3422-2-22-2-222-22-2222-2-2-2-222i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i-22-2200000000000000000000000000000000000-22−2i2i0000000
χ3522-2-22-2-222-22-2222-2-2-2-22−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i-22-22000000000000000000000000000000000002-2−2i2i0000000
χ3622-2-22-2-222-22-2222-2-2-2-22−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i-22-2200000000000000000000000000000000000-222i−2i0000000
χ3722-2-22-2-22-12-22-2-1-11111-12i−2i2i−2i00000000−i−iii−i−iii-11-11−i3−i3−i3−i3i3i3i3i33333−3−3−3−32i−2i2-2000000−ii3−3-11−i3i3000000000000
χ3822-2-22-2-22-12-22-2-1-11111-12i−2i2i−2i00000000−i−iii−i−iii-11-11−i3−i3−i3−i3i3i3i3i33333−3−3−3−3−2i2i-22000000i−i−331-1i3−i3000000000000
χ3922-2-22-2-22-12-22-2-1-11111-12i−2i2i−2i00000000−i−iii−i−iii-11-11i3i3i3i3−i3−i3−i3−i3−3−3−3−333332i−2i2-2000000−ii−33-11i3−i3000000000000
χ4022-2-22-2-22-12-22-2-1-11111-12i−2i2i−2i00000000−i−iii−i−iii-11-11i3i3i3i3−i3−i3−i3−i3−3−3−3−33333−2i2i-22000000i−i3−31-1−i3i3000000000000
χ4122-2-22-2-22-12-22-2-1-11111-1−2i2i−2i2i00000000ii−i−iii−i−i-11-11−i3−i3−i3−i3i3i3i3i3−3−3−3−333332i−2i-22000000−ii3−31-1i3−i3000000000000
χ4222-2-22-2-22-12-22-2-1-11111-1−2i2i−2i2i00000000ii−i−iii−i−i-11-11−i3−i3−i3−i3i3i3i3i3−3−3−3−33333−2i2i2-2000000i−i−33-11−i3i3000000000000
χ4322-2-22-2-22-12-22-2-1-11111-1−2i2i−2i2i00000000ii−i−iii−i−i-11-11i3i3i3i3−i3−i3−i3−i33333−3−3−3−32i−2i-22000000−ii−331-1−i3i3000000000000
χ4422-2-22-2-22-12-22-2-1-11111-1−2i2i−2i2i00000000ii−i−iii−i−i-11-11i3i3i3i3−i3−i3−i3−i33333−3−3−3−3−2i2i2-2000000i−i3−3-11i3−i3000000000000
χ452-22-2-2-222222-2-2-2-2-222-22000000002i2i−2i−2i0000000022-2-2000000002i2i−2i−2i2i2i−2i−2i00002-22-20000000000000000002i−2i00
χ462-22-2-2-222222-2-2-2-2-222-22000000002i2i−2i−2i0000000022-2-2000000002i2i−2i−2i2i2i−2i−2i0000-22-22000000000000000000−2i2i00
χ472-22-2-2-222222-2-2-2-2-222-2200000000−2i−2i2i2i0000000022-2-200000000−2i−2i2i2i−2i−2i2i2i00002-22-2000000000000000000−2i2i00
χ482-22-2-2-222222-2-2-2-2-222-2200000000−2i−2i2i2i0000000022-2-200000000−2i−2i2i2i−2i−2i2i2i0000-22-220000000000000000002i−2i00
χ492-22-2-2-2222-2-222-2-2-222-22000022-2-2000000000000-2-22222-2-222-2-20000000000002-2-2200000000000000002-20000
χ502-22-2-2-2222-2-222-2-2-222-22000022-2-2000000000000-2-22222-2-222-2-2000000000000-222-20000000000000000-220000
χ512-22-2-2-2222-2-222-2-2-222-220000-2-222000000000000-2-222-2-222-2-2220000000000002-2-220000000000000000-220000
χ522-22-2-2-2222-2-222-2-2-222-220000-2-222000000000000-2-222-2-222-2-222000000000000-222-200000000000000002-20000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-400000000-2-2-2-2222222220000000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000000002222-2-2-2-222220000000000000000000000000000000000000000000000
χ554444-4-4-4-4400004-4-44-44-4000022−2222−22000000000000000022−2222−2222−2222−2200000000000000000000000000000000000000
χ564444-4-4-4-4400004-4-44-44-40000−2222−22220000000000000000−2222−2222−2222−222200000000000000000000000000000000000000
χ574444-4-4-4-4-20000-222-22-22000022−2222−220000000023−2323−230000−22−22−22−226−66−66−66−6000000000000000000000000000000
χ584444-4-4-4-4-20000-222-22-22000022−2222−2200000000−2323−23230000−22−22−22−22−66−66−66−66000000000000000000000000000000
χ594444-4-4-4-4-20000-222-22-220000−2222−22220000000023−2323−2300002−22−22−22−2−66−66−66−66000000000000000000000000000000
χ604444-4-4-4-4-20000-222-22-220000−2222−222200000000−2323−232300002−22−22−22−26−66−66−66−6000000000000000000000000000000
χ6144-4-44-4-44-2-44-44-2-22222-24i−4i−4i4i00000000−2i−2i2i2i2i2i−2i−2i2-22-20000000000000000000000000000000000000000000000
χ6244-4-44-4-44-2-44-44-2-22222-2−4i4i4i−4i000000002i2i−2i−2i−2i−2i2i2i2-22-20000000000000000000000000000000000000000000000
χ6344-4-4-444-4400004-44-44-4-40000000022−2222−220000000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ6444-4-4-444-4400004-44-44-4-400000000−2222−222200000000000000000000−2222−222222−2222−22000000000000000000000000000000
χ6544-4-4-444-4-20000-22-22-2220000000022−2222−220000−2i32i32i3−2i30000−i6i6−i6i6i6−i6i6−i6−22−222−22−2000000000000000000000000000000
χ6644-4-4-444-4-20000-22-22-2220000000022−2222−2200002i3−2i3−2i32i30000i6−i6i6−i6−i6i6−i6i6−22−222−22−2000000000000000000000000000000
χ6744-4-4-444-4-20000-22-22-22200000000−2222−22220000−2i32i32i3−2i30000i6−i6i6−i6−i6i6−i6i62−22−2−22−22000000000000000000000000000000
χ6844-4-4-444-4-20000-22-22-22200000000−2222−222200002i3−2i3−2i32i30000−i6i6−i6i6i6−i6i6−i62−22−2−22−22000000000000000000000000000000
χ694-44-444-4-440000-4444-4-4-4000022−22−2222000000000000000022−22−222222−22−222200000000000000000000000000000000000000
χ704-44-444-4-440000-4444-4-4-40000−222222−220000000000000000−222222−22−222222−2200000000000000000000000000000000000000
χ714-44-444-4-4-200002-2-2-2222000022−22−22220000−2i32i3−2i32i300000000−222−2−222−2i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000
χ724-44-444-4-4-200002-2-2-2222000022−22−222200002i3−2i32i3−2i300000000−222−2−222−2−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000
χ734-44-444-4-4-200002-2-2-22220000−222222−220000−2i32i3−2i32i3000000002−2−222−2−22−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000
χ744-44-444-4-4-200002-2-2-22220000−222222−2200002i3−2i32i3−2i3000000002−2−222−2−22i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000
χ754-44-4-4-444-244-4-4222-2-22-2000000004i4i−4i−4i00000000-2-22200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000
χ764-44-4-4-444-244-4-4222-2-22-200000000−4i−4i4i4i00000000-2-222000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000
χ774-44-4-4-444-2-4-444222-2-22-2000044-4-400000000000022-2-2-2-222-2-22200000000000000000000000000000000000000
χ784-44-4-4-444-2-4-444222-2-22-20000-4-44400000000000022-2-222-2-222-2-200000000000000000000000000000000000000
χ794-4-444-44-440000-44-4-444-400000000−2i22i22i2−2i200000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ804-4-444-44-440000-44-4-444-4000000002i2−2i2−2i22i2000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ814-4-444-44-4-200002-222-2-2200000000−2i22i22i2−2i223−23−232300000000−i6i6i6−i6i6−i6−i6i6i2−i2−i2i2−i2i2i2−i2000000000000000000000000000000
χ824-4-444-44-4-200002-222-2-2200000000−2i22i22i2−2i2−232323−2300000000i6−i6−i6i6−i6i6i6−i6i2−i2−i2i2−i2i2i2−i2000000000000000000000000000000
χ834-4-444-44-4-200002-222-2-22000000002i2−2i2−2i22i223−23−232300000000i6−i6−i6i6−i6i6i6−i6−i2i2i2−i2i2−i2−i2i2000000000000000000000000000000
χ844-4-444-44-4-200002-222-2-22000000002i2−2i2−2i22i2−232323−2300000000−i6i6i6−i6i6−i6−i6i6−i2i2i2−i2i2−i2−i2i2000000000000000000000000000000
χ854-4-44-44-4444-4-44-4-44-4-444000000000000000000004-4-440000000000000000000000000000000000000000000000
χ864-4-44-44-444-444-4-4-44-4-44400000000000000000000-444-40000000000000000000000000000000000000000000000
χ874-4-44-44-44-24-4-4422-222-2-200000000000000000000-222-200000000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000000000
χ884-4-44-44-44-24-4-4422-222-2-200000000000000000000-222-2000000002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000000000
χ894-4-44-44-44-2-444-422-222-2-2000000000000000000002-2-22−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000
χ904-4-44-44-44-2-444-422-222-2-2000000000000000000002-2-222i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000

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