Finite Group Databasebeta

← Group #10834031

Character table — Group #10834031

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order1222222234444666666644448888888812121212121212121212121224242424242424242424242424242424224422444466121212121212224444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111111-111-1-111-1-111-1-1-1-111-1-11-1
χ1011111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-111-1-1-1-11111-1-111-11
χ1111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-11-1-111-1-111-1-1-1-11111-1-1-11
χ1211111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-1111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1111-1-1-1-11111-1-1-1-1-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1111-1-1-1-111-1-1111111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111111-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-1-11111-1-11111-1-111-1-1-11
χ17222222222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-2-2-20000000000000000000022-2-2000000000000-2200000000
χ18222222222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-2-2-200000000000000000000-2-2220000000000002-200000000
χ19222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-22222-2-20000000000000000000022-2-20000000000002-200000000
χ20222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-22222-2-200000000000000000000-2-222000000000000-2200000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122220000-2-2-1-1-1-11111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-20000221111-1-1-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-200002-2-1-111-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-2220000-2211-1-111-1-1000000000000
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
χ29222-2-2-2-2222-22-22-22-22-2-22i−2i2i−2i000000002-22i2i−2i−2i2i2i−2i−2i2-200000000000000002-22i−2i0000002-22i−2i0000000000000000
χ30222-2-2-2-2222-22-22-22-22-2-22i−2i2i−2i000000002-22i2i−2i−2i2i2i−2i−2i2-20000000000000000-22−2i2i000000-22−2i2i0000000000000000
χ31222-2-2-2-2222-22-22-22-22-2-2−2i2i−2i2i000000002-2−2i−2i2i2i−2i−2i2i2i2-200000000000000002-2−2i2i0000002-2−2i2i0000000000000000
χ32222-2-2-2-2222-22-22-22-22-2-2−2i2i−2i2i000000002-2−2i−2i2i2i−2i−2i2i2i2-20000000000000000-222i−2i000000-222i−2i0000000000000000
χ33222-2-2-2-222-22-222-22-22-2-22i−2i−2i2i00000000-222i2i−2i−2i−2i−2i2i2i-2200000000000000000000000000000000002-2002i−2i000000
χ34222-2-2-2-222-22-222-22-22-2-22i−2i−2i2i00000000-222i2i−2i−2i−2i−2i2i2i-220000000000000000000000000000000000-2200−2i2i000000
χ35222-2-2-2-222-22-222-22-22-2-2−2i2i2i−2i00000000-22−2i−2i2i2i2i2i−2i−2i-2200000000000000000000000000000000002-200−2i2i000000
χ36222-2-2-2-222-22-222-22-22-2-2−2i2i2i−2i00000000-22−2i−2i2i2i2i2i−2i−2i-220000000000000000000000000000000000-22002i−2i000000
χ37222-2-2-2-22-12-22-2-11-11-1112i−2i2i−2i00000000-11−i−iii−i−iii-11−i3−i3−i3−i3i3i3i3i33333−3−3−3−32-22i−2i000000-11−ii−i3i33−3000000000000
χ38222-2-2-2-22-12-22-2-11-11-1112i−2i2i−2i00000000-11−i−iii−i−iii-11−i3−i3−i3−i3i3i3i3i33333−3−3−3−3-22−2i2i0000001-1i−ii3−i3−33000000000000
χ39222-2-2-2-22-12-22-2-11-11-1112i−2i2i−2i00000000-11−i−iii−i−iii-11i3i3i3i3−i3−i3−i3−i3−3−3−3−333332-22i−2i000000-11−iii3−i3−33000000000000
χ40222-2-2-2-22-12-22-2-11-11-1112i−2i2i−2i00000000-11−i−iii−i−iii-11i3i3i3i3−i3−i3−i3−i3−3−3−3−33333-22−2i2i0000001-1i−i−i3i33−3000000000000
χ41222-2-2-2-22-12-22-2-11-11-111−2i2i−2i2i00000000-11ii−i−iii−i−i-11−i3−i3−i3−i3i3i3i3i3−3−3−3−333332-2−2i2i000000-11i−i−i3i3−33000000000000
χ42222-2-2-2-22-12-22-2-11-11-111−2i2i−2i2i00000000-11ii−i−iii−i−i-11−i3−i3−i3−i3i3i3i3i3−3−3−3−33333-222i−2i0000001-1−iii3−i33−3000000000000
χ43222-2-2-2-22-12-22-2-11-11-111−2i2i−2i2i00000000-11ii−i−iii−i−i-11i3i3i3i3−i3−i3−i3−i33333−3−3−3−32-2−2i2i000000-11i−ii3−i33−3000000000000
χ44222-2-2-2-22-12-22-2-11-11-111−2i2i−2i2i00000000-11ii−i−iii−i−i-11i3i3i3i3−i3−i3−i3−i33333−3−3−3−3-222i−2i0000001-1−ii−i3i3−33000000000000
χ452-2-222-2-22222-2-2-2-222-2-2200002i2i−2i−2i00002200000000-2-22i2i−2i−2i2i2i−2i−2i0000000000002-22-200000000000000002i−2i0000
χ462-2-222-2-22222-2-2-2-222-2-2200002i2i−2i−2i00002200000000-2-22i2i−2i−2i2i2i−2i−2i000000000000-22-220000000000000000−2i2i0000
χ472-2-222-2-22222-2-2-2-222-2-220000−2i−2i2i2i00002200000000-2-2−2i−2i2i2i−2i−2i2i2i0000000000002-22-20000000000000000−2i2i0000
χ482-2-222-2-22222-2-2-2-222-2-220000−2i−2i2i2i00002200000000-2-2−2i−2i2i2i−2i−2i2i2i000000000000-22-2200000000000000002i−2i0000
χ492-2-222-2-222-2-222-2-222-2-220000000022-2-2-2-200000000220000000022-2-222-2-200002-2-220000000000000000002-200
χ502-2-222-2-222-2-222-2-222-2-220000000022-2-2-2-200000000220000000022-2-222-2-20000-222-2000000000000000000-2200
χ512-2-222-2-222-2-222-2-222-2-2200000000-2-222-2-2000000002200000000-2-222-2-22200002-2-22000000000000000000-2200
χ522-2-222-2-222-2-222-2-222-2-2200000000-2-222-2-2000000002200000000-2-222-2-2220000-222-20000000000000000002-200
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
χ55444-4-4-4-44-2-44-44-22-22-2224i−4i−4i4i000000002-2−2i−2i2i2i2i2i−2i−2i2-20000000000000000000000000000000000000000000000
χ56444-4-4-4-44-2-44-44-22-22-222−4i4i4i−4i000000002-22i2i−2i−2i−2i−2i2i2i2-20000000000000000000000000000000000000000000000
χ5744-44-4-44-4400004-4-44-44-400000000−2i22i2−2i22i200000000000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000
χ5844-44-4-44-4400004-4-44-44-4000000002i2−2i22i2−2i2000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000
χ5944-44-4-44-4-20000-222-22-2200000000−2i22i2−2i22i200−2i32i3−2i32i30000006−66−66−66−6i2−i2i2−i2i2−i2i2−i2000000000000000000000000000000
χ6044-44-4-44-4-20000-222-22-2200000000−2i22i2−2i22i2002i3−2i32i3−2i3000000−66−66−66−66i2−i2i2−i2i2−i2i2−i2000000000000000000000000000000
χ6144-44-4-44-4-20000-222-22-22000000002i2−2i22i2−2i200−2i32i3−2i32i3000000−66−66−66−66−i2i2−i2i2−i2i2−i2i2000000000000000000000000000000
χ6244-44-4-44-4-20000-222-22-22000000002i2−2i22i2−2i2002i3−2i32i3−2i30000006−66−66−66−6−i2i2−i2i2−i2i2−i2i2000000000000000000000000000000
χ6344-4-444-4-44000044-4-4-4-440000−2i22i2−2i22i20000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ6444-4-444-4-44000044-4-4-4-4400002i2−2i22i2−2i200000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ6544-4-444-4-4-20000-2-22222-20000−2i22i2−2i22i200000023−23−2323000000i2−i2i2−i2−i2i2−i2i2i6−i6i6−i6−i6i6−i6i6000000000000000000000000000000
χ6644-4-444-4-4-20000-2-22222-20000−2i22i2−2i22i2000000−232323−23000000i2−i2i2−i2−i2i2−i2i2−i6i6−i6i6i6−i6i6−i6000000000000000000000000000000
χ6744-4-444-4-4-20000-2-22222-200002i2−2i22i2−2i200000023−23−2323000000−i2i2−i2i2i2−i2i2−i2−i6i6−i6i6i6−i6i6−i6000000000000000000000000000000
χ6844-4-444-4-4-20000-2-22222-200002i2−2i22i2−2i2000000−232323−23000000−i2i2−i2i2i2−i2i2−i2i6−i6i6−i6−i6i6−i6i6000000000000000000000000000000
χ694-444-44-4-440000-44-444-4-400000000−2i22i22i2−2i200000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ704-444-44-4-440000-44-444-4-4000000002i2−2i2−2i22i2000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ714-444-44-4-4-200002-22-2-22200000000−2i22i22i2−2i200000023−2323−2300i6−i6−i6i6i6−i6−i6i6i2−i2−i2i2i2−i2−i2i2000000000000000000000000000000
χ724-444-44-4-4-200002-22-2-22200000000−2i22i22i2−2i2000000−2323−232300−i6i6i6−i6−i6i6i6−i6i2−i2−i2i2i2−i2−i2i2000000000000000000000000000000
χ734-444-44-4-4-200002-22-2-222000000002i2−2i2−2i22i200000023−2323−2300−i6i6i6−i6−i6i6i6−i6−i2i2i2−i2−i2i2i2−i2000000000000000000000000000000
χ744-444-44-4-4-200002-22-2-222000000002i2−2i2−2i22i2000000−2323−232300i6−i6−i6i6i6−i6−i6i6−i2i2i2−i2−i2i2i2−i2000000000000000000000000000000
χ754-44-44-44-440000-4-4-4-4444000022−22−2222000000000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ764-44-44-44-440000-4-4-4-44440000−222222−220000000000000000−222222−2222−22−222200000000000000000000000000000000000000
χ774-44-44-44-4-200002222-2-2-2000022−22−22220000000000−2i32i32i3−2i300−222−22−2−22−i6i6i6−i6i6−i6−i6i6000000000000000000000000000000
χ784-44-44-44-4-200002222-2-2-2000022−22−222200000000002i3−2i3−2i32i300−222−22−2−22i6−i6−i6i6−i6i6i6−i6000000000000000000000000000000
χ794-44-44-44-4-200002222-2-2-20000−222222−220000000000−2i32i32i3−2i3002−2−22−222−2i6−i6−i6i6−i6i6i6−i6000000000000000000000000000000
χ804-44-44-44-4-200002222-2-2-20000−222222−2200000000002i3−2i3−2i32i3002−2−22−222−2−i6i6i6−i6i6−i6−i6i6000000000000000000000000000000
χ814-4-444-4-44-244-4-422-2-222-200004i4i−4i−4i0000-2-20000000022−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000
χ824-4-444-4-44-244-4-422-2-222-20000−4i−4i4i4i0000-2-200000000222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000
χ834-4-444-4-44-2-4-44422-2-222-20000000044-4-42200000000-2-200000000-2-222-2-222000000000000000000000000000000
χ844-4-444-4-44-2-4-44422-2-222-200000000-4-4442200000000-2-20000000022-2-222-2-2000000000000000000000000000000
χ854-4-4-4-444444-4-44-444-4-44-40000000000004-400000000-440000000000000000000000000000000000000000000000
χ864-4-4-4-44444-444-4-444-4-44-4000000000000-44000000004-40000000000000000000000000000000000000000000000
χ874-4-4-4-4444-24-4-442-2-222-22000000000000-22000000002-22323−23−23−23−23232300000000000000000000000000000000000000
χ884-4-4-4-4444-24-4-442-2-222-22000000000000-22000000002-2−23−2323232323−23−2300000000000000000000000000000000000000
χ894-4-4-4-4444-2-444-42-2-222-220000000000002-200000000-22000000002323−23−23−23−232323000000000000000000000000000000
χ904-4-4-4-4444-2-444-42-2-222-220000000000002-200000000-2200000000−23−2323232323−23−23000000000000000000000000000000

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