Finite Group Databasebeta

← Group #10829907

Character table — Group #10829907

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222224444444444444444444444444488888888888888888888888888888888242424242424242448484848
order1222223444466644444444661212121212121212121212121212121222444444446666121212121212121212121212121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111-1-1-1-11111111111111-11-11-1-1-11-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111-1-1-1-111-1-1-1-11111111111111-11-11-1-1-11-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ7111111111111111111-1-1-1-111-1-1-1-1111111111111-11-11-11-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ8111111111111111111-1-1-1-111-1-1-1-1111111111111-11-11-11-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ911111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-11-11-1
χ1011111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-11-11
χ1111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-11-11
χ1211111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111111-11-1
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-11111-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-11111-111-1-1-1-111-1-1111111-1-1-1-111-1-11111-1-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-111-11-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-111-111-1
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-111-11-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-11-1-11
χ172222222-2-2-2-222222-2-222-2-222-2-2-2-2-2-2-2-22222-2-2-2-20000002-200000000002222-2-200000000000000000000
χ182222222-2-2-2-222222-2-2-2-222222222-2-2-2-22222-2-2-2-2000000-220000000000-2-2-2-22200000000000000000000
χ192222222-2-2-2-2222-2-22222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222000000-22000000000022-2-22200000000000000000000
χ202222222-2-2-2-2222-2-222-2-222222222-2-2-2-2-2-2-2-222220000002-20000000000-2-222-2-200000000000000000000
χ21222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-211111111-1-1-1-1-1-111111111000000000000
χ23222222-12222-1-1-12222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1-1-12-22-22-2-2-22-2-1-111-1-111111111-1-1-1-11111000000000000
χ24222222-12222-1-1-12222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-22-22-22-2-2-2211-1-111-1-11111111111-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-2-2-222-1-1-1-11111-1-11111-1-111-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-111111111-2-22222-2-2-2-21111-1-1-1-1-1-1111111-1-111-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-1111111112-2-22-22222-2-1-11111-1-111-1-1-1-1-1-11111-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-111111111-222-22-222-2211-1-1-1-11111-1-1-1-111-1-1-1-111000000000000
χ29222222-1-2-2-2-2-1-1-122-2-222-2-2-1-111111111-1-1-1-111110000002-200−i3i3−i3i3−i3i3−i3i3-1-1-1-111−i3i3−i3i3−i3i3−i3i3000000000000
χ30222222-1-2-2-2-2-1-1-122-2-222-2-2-1-111111111-1-1-1-111110000002-200i3−i3i3−i3i3−i3i3−i3-1-1-1-111i3−i3i3−i3i3−i3i3−i3000000000000
χ31222222-1-2-2-2-2-1-1-122-2-2-2-222-1-1-1-1-1-11111-1-1-1-11111000000-2200−i3i3i3−i3−i3i3i3−i31111-1-1−i3i3−i3i3i3−i3i3−i3000000000000
χ32222222-1-2-2-2-2-1-1-122-2-2-2-222-1-1-1-1-1-11111-1-1-1-11111000000-2200i3−i3−i3i3i3−i3−i3i31111-1-1i3−i3i3−i3−i3i3−i3i3000000000000
χ33222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-1111111111111-1-1-1-1000000-2200−i3i3−i3i3i3−i3i3−i3-1-111-1-1−i3i3i3−i3−i3i3i3−i3000000000000
χ34222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-1111111111111-1-1-1-1000000-2200i3−i3i3−i3−i3i3−i3i3-1-111-1-1i3−i3−i3i3i3−i3−i3i3000000000000
χ35222222-1-2-2-2-2-1-1-1-2-222-2-222-1-1-1-1-1-111111111-1-1-1-10000002-200−i3i3i3−i3i3−i3−i3i311-1-111−i3i3i3−i3i3−i3−i3i3000000000000
χ36222222-1-2-2-2-2-1-1-1-2-222-2-222-1-1-1-1-1-111111111-1-1-1-10000002-200i3−i3−i3i3−i3i3i3−i311-1-111i3−i3−i3i3−i3i3i3−i3000000000000
χ372222-2-222-22-222200002-22-2-2-222-2-222-2-2000000000022-2-200000000-2-2-2-22-2000000220022000000000000
χ382222-2-222-22-222200002-22-2-2-222-2-222-2-20000000000-2-2220000000022222-2000000-2-200-2-2000000000000
χ392222-2-222-22-22220000-22-22-2-2-2-22222-2-200000000002-2-2200000000-2-222-220000002200-2-2000000000000
χ402222-2-222-22-22220000-22-22-2-2-2-22222-2-20000000000-222-20000000022-2-2-22000000-2-20022000000000000
χ412222-2-22-22-2222200002-2-22-2-2-2-222-2-222000000002-2000000-2222-2-200002-20000-2-2002200000000000000
χ422222-2-22-22-2222200002-2-22-2-2-2-222-2-22200000000-220000002-2-2-22200002-200002200-2-200000000000000
χ432222-2-22-22-222220000-222-2-2-222-2-2-2-2220000000022000000-2-222220000-220000-2-200-2-200000000000000
χ442222-2-22-22-222220000-222-2-2-222-2-2-2-22200000000-2-200000022-2-2-2-20000-22000022002200000000000000
χ452222-2-2-12-22-2-1-1-100002-22-211-1-111-1-111−i3−i3i3i3−i3−i3i3i30022-2-20000−i3i3i3−i31111-11−i3i3−i3i3i3−i3-1-1−i3i3-1-1000000000000
χ462222-2-2-12-22-2-1-1-100002-22-211-1-111-1-111−i3−i3i3i3−i3−i3i3i300-2-2220000i3−i3−i3i3-1-1-1-1-11−i3i3−i3i3−i3i311i3−i311000000000000
χ472222-2-2-12-22-2-1-1-100002-22-211-1-111-1-111i3i3−i3−i3i3i3−i3−i30022-2-20000i3−i3−i3i31111-11i3−i3i3−i3−i3i3-1-1i3−i3-1-1000000000000
χ482222-2-2-12-22-2-1-1-100002-22-211-1-111-1-111i3i3−i3−i3i3i3−i3−i300-2-2220000−i3i3i3−i3-1-1-1-1-11i3−i3i3−i3i3−i311−i3i311000000000000
χ492222-2-2-12-22-2-1-1-10000-22-221111-1-1-1-111−i3−i3i3i3−i3−i3i3i3002-2-220000−i3i3−i3i311-1-11-1i3−i3i3−i3i3−i3-1-1i3−i311000000000000
χ502222-2-2-12-22-2-1-1-10000-22-221111-1-1-1-111−i3−i3i3i3−i3−i3i3i300-222-20000i3−i3i3−i3-1-1111-1i3−i3i3−i3−i3i311−i3i3-1-1000000000000
χ512222-2-2-12-22-2-1-1-10000-22-221111-1-1-1-111i3i3−i3−i3i3i3−i3−i3002-2-220000i3−i3i3−i311-1-11-1−i3i3−i3i3−i3i3-1-1−i3i311000000000000
χ522222-2-2-12-22-2-1-1-10000-22-221111-1-1-1-111i3i3−i3−i3i3i3−i3−i300-222-20000−i3i3−i3i3-1-1111-1−i3i3−i3i3i3−i311i3−i3-1-1000000000000
χ532222-2-2-1-22-22-1-1-100002-2-221111-1-111-1-1−i3−i3i3i3i3i3−i3−i32-2000000-22-1-111i3−i3i3−i3-11−i3i3i3−i311−i3i3-1-1−i3i3000000000000
χ542222-2-2-1-22-22-1-1-100002-2-221111-1-111-1-1−i3−i3i3i3i3i3−i3−i3-220000002-211-1-1−i3i3−i3i3-11−i3i3i3−i3-1-1i3−i311i3−i3000000000000
χ552222-2-2-1-22-22-1-1-100002-2-221111-1-111-1-1i3i3−i3−i3−i3−i3i3i32-2000000-22-1-111−i3i3−i3i3-11i3−i3−i3i311i3−i3-1-1i3−i3000000000000
χ562222-2-2-1-22-22-1-1-100002-2-221111-1-111-1-1i3i3−i3−i3−i3−i3i3i3-220000002-211-1-1i3−i3i3−i3-11i3−i3−i3i3-1-1−i3i311−i3i3000000000000
χ572222-2-2-1-22-22-1-1-10000-222-211-1-11111-1-1−i3−i3i3i3i3i3−i3−i322000000-2-2-1-1-1-1i3−i3−i3i31-1i3−i3−i3i311−i3i311i3−i3000000000000
χ582222-2-2-1-22-22-1-1-10000-222-211-1-11111-1-1−i3−i3i3i3i3i3−i3−i3-2-2000000221111−i3i3i3−i31-1i3−i3−i3i3-1-1i3−i3-1-1−i3i3000000000000
χ592222-2-2-1-22-22-1-1-10000-222-211-1-11111-1-1i3i3−i3−i3−i3−i3i3i322000000-2-2-1-1-1-1−i3i3i3−i31-1−i3i3i3−i311i3−i311−i3i3000000000000
χ602222-2-2-1-22-22-1-1-10000-222-211-1-11111-1-1i3i3−i3−i3−i3−i3i3i3-2-2000000221111i3−i3−i3i31-1−i3i3i3−i3-1-1−i3i3-1-1i3−i3000000000000
χ612-2-222-222-2-22-22-22i−2i2i−2i00002-200002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000002-2002i−2i0000
χ622-2-222-222-2-22-22-22i−2i2i−2i00002-200002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000-2200−2i2i0000
χ632-2-222-222-2-22-22-2−2i2i−2i2i00002-200002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000002-200−2i2i0000
χ642-2-222-222-2-22-22-2−2i2i−2i2i00002-200002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000-22002i−2i0000
χ652-2-222-22-222-2-22-22i−2i−2i2i00002-20000-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000002i−2i002-2000000
χ662-2-222-22-222-2-22-22i−2i−2i2i00002-20000-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000−2i2i00-22000000
χ672-2-222-22-222-2-22-2−2i2i2i−2i00002-20000-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000002i−2i00-22000000
χ682-2-222-22-222-2-22-2−2i2i2i−2i00002-20000-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000−2i2i002-2000000
χ694-4-444-4-24-4-442-224i−4i4i−4i0000-220000-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000
χ704-4-444-4-24-4-442-22−4i4i−4i4i0000-220000-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ714-4-444-4-2-444-42-224i−4i−4i4i0000-2200002-22-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ724-4-444-4-2-444-42-22−4i4i4i−4i0000-2200002-22-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000
χ734-4-44-44444-4-4-44-400000000-4400004-4-440000000000000000000000000000000000000000000000000000
χ744-4-44-444-4-444-44-400000000-440000-444-40000000000000000000000000000000000000000000000000000
χ754-4-44-44-244-4-42-22000000002-20000-222-223−23−232323−23−232300000000000000000000000000000000000000000000
χ764-4-44-44-244-4-42-22000000002-20000-222-2−232323−23−232323−2300000000000000000000000000000000000000000000
χ774-4-44-44-2-4-4442-22000000002-200002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000
χ784-4-44-44-2-4-4442-22000000002-200002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000
χ7988-8-80080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-4000044-400000000000043−4300000000000000000000000000000000000000000000000000000000
χ8188-8-800-4000044-4000000000000−434300000000000000000000000000000000000000000000000000000000
χ828-88-800800008-8-80000000000000000000000000000000000000000000000000000000000000000000000
χ838-88-800-40000-4440000000000−4i34i30000000000000000000000000000000000000000000000000000000000
χ848-88-800-40000-44400000000004i3−4i30000000000000000000000000000000000000000000000000000000000

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