Finite Group Databasebeta

← Group #10833984

Character table — Group #10833984

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order12222222344446666666444488888888121212121212121212121212242424242424242424242424242424242244224424666612121212444444888844
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
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
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111111111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111111-11111-1-1-1-1-1-111-1-111-1-1-11
χ1011111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-1-1-111-1-111-1-1111-1
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
χ1311111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1111-1-1-1-111-1-111-1-1-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1111-1-1-1-11111-1-11111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111111-1-1-11111-1-1-1-1-1-111-1-111-11
χ1611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-1-11111-1-11111-1-111-1-11-1
χ17222222222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-2-2-20000000000000000000022-2-20000000000-220000000000
χ18222222222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-2-2-200000000000000000000-2-22200000000002-20000000000
χ19222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-22222-2-20000000000000000000022-2-200000000002-20000000000
χ20222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-22222-2-200000000000000000000-2-2220000000000-220000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-200002-2-1-1-1-11111000000000000
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
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-122-2-20000-22-1-11111-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1-2-22200002-211-1-1-1-111000000000000
χ2922-2-222-2-222-22-222-22-2-2-22i−2i2i−2i000000002-22i2i−2i−2i2i2i−2i−2i2-200000000000000002-22i−2i0000002-2002i−2i00000000000000
χ3022-2-222-2-222-22-222-22-2-2-22i−2i2i−2i000000002-22i2i−2i−2i2i2i−2i−2i2-20000000000000000-22−2i2i000000-2200−2i2i00000000000000
χ3122-2-222-2-222-22-222-22-2-2-2−2i2i−2i2i000000002-2−2i−2i2i2i−2i−2i2i2i2-200000000000000002-2−2i2i0000002-200−2i2i00000000000000
χ3222-2-222-2-222-22-222-22-2-2-2−2i2i−2i2i000000002-2−2i−2i2i2i−2i−2i2i2i2-20000000000000000-222i−2i000000-22002i−2i00000000000000
χ3322-2-222-2-22-22-2222-22-2-2-22i−2i−2i2i00000000-222i2i−2i−2i−2i−2i2i2i-220000000000000000000000000000000000002-22i−2i000000
χ3422-2-222-2-22-22-2222-22-2-2-22i−2i−2i2i00000000-222i2i−2i−2i−2i−2i2i2i-22000000000000000000000000000000000000-22−2i2i000000
χ3522-2-222-2-22-22-2222-22-2-2-2−2i2i2i−2i00000000-22−2i−2i2i2i2i2i−2i−2i-220000000000000000000000000000000000002-2−2i2i000000
χ3622-2-222-2-22-22-2222-22-2-2-2−2i2i2i−2i00000000-22−2i−2i2i2i2i2i−2i−2i-22000000000000000000000000000000000000-222i−2i000000
χ3722-2-222-2-2-12-22-2-1-11-11112i−2i2i−2i00000000-11−i−iii−i−iii-11−i3−i3−i3−i3i3i3i3i33333−3−3−3−32-22i−2i000000-11−i3i3−ii3−3000000000000
χ3822-2-222-2-2-12-22-2-1-11-11112i−2i2i−2i00000000-11−i−iii−i−iii-11−i3−i3−i3−i3i3i3i3i33333−3−3−3−3-22−2i2i0000001-1i3−i3i−i−33000000000000
χ3922-2-222-2-2-12-22-2-1-11-11112i−2i2i−2i00000000-11−i−iii−i−iii-11i3i3i3i3−i3−i3−i3−i3−3−3−3−333332-22i−2i000000-11i3−i3−ii−33000000000000
χ4022-2-222-2-2-12-22-2-1-11-11112i−2i2i−2i00000000-11−i−iii−i−iii-11i3i3i3i3−i3−i3−i3−i3−3−3−3−33333-22−2i2i0000001-1−i3i3i−i3−3000000000000
χ4122-2-222-2-2-12-22-2-1-11-1111−2i2i−2i2i00000000-11ii−i−iii−i−i-11−i3−i3−i3−i3i3i3i3i3−3−3−3−333332-2−2i2i000000-11−i3i3i−i−33000000000000
χ4222-2-222-2-2-12-22-2-1-11-1111−2i2i−2i2i00000000-11ii−i−iii−i−i-11−i3−i3−i3−i3i3i3i3i3−3−3−3−33333-222i−2i0000001-1i3−i3−ii3−3000000000000
χ4322-2-222-2-2-12-22-2-1-11-1111−2i2i−2i2i00000000-11ii−i−iii−i−i-11i3i3i3i3−i3−i3−i3−i33333−3−3−3−32-2−2i2i000000-11i3−i3i−i3−3000000000000
χ4422-2-222-2-2-12-22-2-1-11-1111−2i2i−2i2i00000000-11ii−i−iii−i−i-11i3i3i3i3−i3−i3−i3−i33333−3−3−3−3-222i−2i0000001-1−i3i3−ii−33000000000000
χ452-2-22-222-2222-2-2-2-2-2222-2000000002i2i−2i−2i2200000000-2-2000000002i2i−2i−2i2i2i−2i−2i00002-22-20000000000000000002i−2i00
χ462-2-22-222-2222-2-2-2-2-2222-2000000002i2i−2i−2i2200000000-2-2000000002i2i−2i−2i2i2i−2i−2i0000-22-22000000000000000000−2i2i00
χ472-2-22-222-2222-2-2-2-2-2222-200000000−2i−2i2i2i2200000000-2-200000000−2i−2i2i2i−2i−2i2i2i00002-22-2000000000000000000−2i2i00
χ482-2-22-222-2222-2-2-2-2-2222-200000000−2i−2i2i2i2200000000-2-200000000−2i−2i2i2i−2i−2i2i2i0000-22-220000000000000000002i−2i00
χ492-2-22-222-22-2-222-2-2-2222-2000022-2-20000-2-2000000002222-2-222-2-20000000000002-2-2200000000000000002-20000
χ502-2-22-222-22-2-222-2-2-2222-2000022-2-20000-2-2000000002222-2-222-2-2000000000000-222-20000000000000000-220000
χ512-2-22-222-22-2-222-2-2-2222-20000-2-2220000-2-20000000022-2-222-2-2220000000000002-2-220000000000000000-220000
χ522-2-22-222-22-2-222-2-2-2222-20000-2-2220000-2-20000000022-2-222-2-222000000000000-222-200000000000000002-20000
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
χ554444-4-4-4-4400004-44-44-4-4000022−2222−22000000000000000022−2222−2222−2222−2200000000000000000000000000000000000000
χ564444-4-4-4-4400004-44-44-4-40000−2222−22220000000000000000−2222−2222−2222−222200000000000000000000000000000000000000
χ574444-4-4-4-4-20000-22-22-222000022−2222−22000000000023−2323−2300−22−22−22−226−66−66−66−6000000000000000000000000000000
χ584444-4-4-4-4-20000-22-22-222000022−2222−220000000000−2323−232300−22−22−22−22−66−66−66−66000000000000000000000000000000
χ594444-4-4-4-4-20000-22-22-2220000−2222−2222000000000023−2323−23002−22−22−22−2−66−66−66−66000000000000000000000000000000
χ604444-4-4-4-4-20000-22-22-2220000−2222−22220000000000−2323−2323002−22−22−22−26−66−66−66−6000000000000000000000000000000
χ6144-4-444-4-4-2-44-44-2-22-22224i−4i−4i4i000000002-2−2i−2i2i2i2i2i−2i−2i2-20000000000000000000000000000000000000000000000
χ6244-4-444-4-4-2-44-44-2-22-2222−4i4i4i−4i000000002-22i2i−2i−2i−2i−2i2i2i2-20000000000000000000000000000000000000000000000
χ6344-4-4-4-444400004-4-4-4-4440000000022−2222−220000000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ6444-4-4-4-444400004-4-4-4-44400000000−2222−222200000000000000000000−2222−222222−2222−22000000000000000000000000000000
χ6544-4-4-4-444-20000-22222-2-20000000022−2222−22000000−2i32i32i3−2i300−i6i6−i6i6i6−i6i6−i6−22−222−22−2000000000000000000000000000000
χ6644-4-4-4-444-20000-22222-2-20000000022−2222−220000002i3−2i3−2i32i300i6−i6i6−i6−i6i6−i6i6−22−222−22−2000000000000000000000000000000
χ6744-4-4-4-444-20000-22222-2-200000000−2222−2222000000−2i32i32i3−2i300i6−i6i6−i6−i6i6−i6i62−22−2−22−22000000000000000000000000000000
χ6844-4-4-4-444-20000-22222-2-200000000−2222−22220000002i3−2i3−2i32i300−i6i6−i6i6i6−i6i6−i62−22−2−22−22000000000000000000000000000000
χ694-44-44-44-440000-444-4-44-400000000−2i22i22i2−2i200000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ704-44-44-44-440000-444-4-44-4000000002i2−2i2−2i22i2000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ714-44-44-44-4-200002-2-222-2200000000−2i22i22i2−2i20023−2323−23000000i6−i6−i6i6−i6i6i6−i6i2−i2−i2i2−i2i2i2−i2000000000000000000000000000000
χ724-44-44-44-4-200002-2-222-2200000000−2i22i22i2−2i200−2323−2323000000−i6i6i6−i6i6−i6−i6i6i2−i2−i2i2−i2i2i2−i2000000000000000000000000000000
χ734-44-44-44-4-200002-2-222-22000000002i2−2i2−2i22i20023−2323−23000000−i6i6i6−i6i6−i6−i6i6−i2i2i2−i2i2−i2−i2i2000000000000000000000000000000
χ744-44-44-44-4-200002-2-222-22000000002i2−2i2−2i22i200−2323−2323000000i6−i6−i6i6−i6i6i6−i6−i2i2i2−i2i2−i2−i2i2000000000000000000000000000000
χ754-44-4-44-4444-4-44-4-444-4-440000000000004-400000000-440000000000000000000000000000000000000000000000
χ764-44-4-44-444-444-4-4-444-4-44000000000000-44000000004-40000000000000000000000000000000000000000000000
χ774-44-4-44-44-24-4-4422-2-222-2000000000000-22000000002-200000000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000000000
χ784-44-4-44-44-24-4-4422-2-222-2000000000000-22000000002-2000000002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000000000
χ794-44-4-44-44-2-444-422-2-222-20000000000002-200000000-22−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000
χ804-44-4-44-44-2-444-422-2-222-20000000000002-200000000-222i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000
χ814-4-444-4-4440000-44-4-44-44000022−22−2222000000000000000022−22−222222−22−222200000000000000000000000000000000000000
χ824-4-444-4-4440000-44-4-44-440000−222222−220000000000000000−222222−22−222222−2200000000000000000000000000000000000000
χ834-4-444-4-44-200002-222-22-2000022−22−2222000000−2i32i32i3−2i3000000−222−2−222−2−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000
χ844-4-444-4-44-200002-222-22-2000022−22−22220000002i3−2i3−2i32i3000000−222−2−222−2i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000
χ854-4-444-4-44-200002-222-22-20000−222222−22000000−2i32i32i3−2i30000002−2−222−2−22i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000
χ864-4-444-4-44-200002-222-22-20000−222222−220000002i3−2i3−2i32i30000002−2−222−2−22−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000
χ874-4-44-444-4-244-4-4222-2-2-22000000004i4i−4i−4i-2-2000000002200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000
χ884-4-44-444-4-244-4-4222-2-2-2200000000−4i−4i4i4i-2-20000000022000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000
χ894-4-44-444-4-2-4-444222-2-2-22000044-4-400002200000000-2-2-2-222-2-22200000000000000000000000000000000000000
χ904-4-44-444-4-2-4-444222-2-2-220000-4-44400002200000000-2-222-2-222-2-200000000000000000000000000000000000000

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