Finite Group Databasebeta

← Group #10828032

Character table — Group #10828032

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222224444444444444444444444444488888888888888888888888888888888242424242424242448484848
order1222223444466622444444661212121212121212121212121212121222224444446666666666121212121212121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-11-11-111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-11-11-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-11-11-1111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-11-11-1111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ911111111111111-1-1-1-11111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11-11-1
χ1011111111111111-1-1-1-11111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11-11
χ1111111111111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-11-11
χ1211111111111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-111-111-1
χ1611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1-11111-1-1111111-1-1-1-1-1-111-1-11111-1-11-1-11
χ172222222-2-2-2-222222-2-222-2-222-2-2-2-2-2-2-2-22222-2-2-2-22-2000000002222-2-20000000000000000000000000000
χ182222222-2-2-2-222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-220000000022-2-2220000000000000000000000000000
χ192222222-2-2-2-2222-2-22222-2-222-2-2-2-222222222-2-2-2-2-2200000000-2-2-2-2220000000000000000000000000000
χ202222222-2-2-2-2222-2-222-2-22222-2-2-2-22222-2-2-2-222222-200000000-2-222-2-20000000000000000000000000000
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
χ22222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111000000000000
χ23222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-22-22-22-22-2-1-11111-1-111-1-1-1-11111-1-111000000000000
χ24222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2-22-22-22-22-1-1111111-1-11111-1-1-1-111-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-222-2-222-2-2111111-1-1-1-111111111-1-1-1-1000000000000
χ26222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2-222-2-2221111111111-1-1-1-1-1-1-1-11111000000000000
χ27222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1111111111111222-2-222-2-2211-1-1-1-1-1-1111111-1-1-1-1-1-111000000000000
χ28222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111122-222-2-222-211-1-1-1-111-1-1-1-1-1-1111111-1-1000000000000
χ29222222-1-2-2-2-2-1-1-122-2-222-2-2-1-111111111-1-1-1-111112-200000000-1-1-1-111−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3i3−i3i3000000000000
χ30222222-1-2-2-2-2-1-1-122-2-222-2-2-1-111111111-1-1-1-111112-200000000-1-1-1-111i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3−i3i3−i3000000000000
χ31222222-1-2-2-2-2-1-1-122-2-2-2-222-1-1111111111111-1-1-1-1-2200000000-1-111-1-1−i3i3i3−i3−i3−i3i3i3i3i3−i3−i3−i3i3i3−i3000000000000
χ32222222-1-2-2-2-2-1-1-122-2-2-2-222-1-1111111111111-1-1-1-1-2200000000-1-111-1-1i3−i3−i3i3i3i3−i3−i3−i3−i3i3i3i3−i3−i3i3000000000000
χ33222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-11111-1-1-1-1-1-1-1-11111-22000000001111-1-1−i3i3−i3i3i3i3−i3−i3i3i3−i3−i3−i3i3−i3i3000000000000
χ34222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-11111-1-1-1-1-1-1-1-11111-22000000001111-1-1i3−i3i3−i3−i3−i3i3i3−i3−i3i3i3i3−i3i3−i3000000000000
χ35222222-1-2-2-2-2-1-1-1-2-222-2-222-1-11111-1-1-1-11111-1-1-1-12-20000000011-1-111−i3i3i3−i3i3i3−i3−i3−i3−i3i3i3−i3i3i3−i3000000000000
χ36222222-1-2-2-2-2-1-1-1-2-222-2-222-1-11111-1-1-1-11111-1-1-1-12-20000000011-1-111i3−i3−i3i3−i3−i3i3i3i3i3−i3−i3i3−i3−i3i3000000000000
χ372222-2-2222-2-22222-22-20000-2-222-2-222-2-2000000000002020-20-22-20000002200002-22-200-2-2000000000000
χ382222-2-2222-2-22222-22-20000-2-222-2-222-2-200000000000-20-202022-2000000-2-20000-22-220022000000000000
χ392222-2-2222-2-2222-22-220000-2-222-2-2-2-2220000000000020-20-202-22000000220000-22-2200-2-2000000000000
χ402222-2-2222-2-2222-22-220000-2-222-2-2-2-22200000000000-202020-2-22000000-2-200002-22-20022000000000000
χ412222-2-22-2-2222222-2-220000-2-2-2-222-2-222000000000020-20-20202-2000022002-22-20000-2-200000000000000
χ422222-2-22-2-2222222-2-220000-2-2-2-222-2-2220000000000-202020-202-20000-2-200-22-2200002200000000000000
χ432222-2-22-2-222222-222-20000-2-2-2-22222-2-200000000002020-20-20-2200002200-22-220000-2-200000000000000
χ442222-2-22-2-222222-222-20000-2-2-2-22222-2-20000000000-20-202020-220000-2-2002-22-200002200000000000000
χ452222-2-2-122-2-2-1-1-12-22-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i30002020-20-2-11−i3i3−i3i3−i3i3-1-1−i3i3i3−i3-11-11i3−i311000000000000
χ462222-2-2-122-2-2-1-1-12-22-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i3000-20-20202-11−i3i3−i3i3i3−i311i3−i3−i3i31-11-1−i3i3-1-1000000000000
χ472222-2-2-122-2-2-1-1-12-22-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i30002020-20-2-11i3−i3i3−i3i3−i3-1-1i3−i3−i3i3-11-11−i3i311000000000000
χ482222-2-2-122-2-2-1-1-12-22-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i3000-20-20202-11i3−i3i3−i3−i3i311−i3i3i3−i31-11-1i3−i3-1-1000000000000
χ492222-2-2-122-2-2-1-1-1-22-22000011-1-11111-1-1−i3−i3i3i3−i3−i3i3i300020-20-2021-1i3−i3i3−i3−i3i3-1-1i3−i3−i3i31-11-1i3−i311000000000000
χ502222-2-2-122-2-2-1-1-1-22-22000011-1-11111-1-1−i3−i3i3i3−i3−i3i3i3000-202020-21-1i3−i3i3−i3i3−i311−i3i3i3−i3-11-11−i3i3-1-1000000000000
χ512222-2-2-122-2-2-1-1-1-22-22000011-1-11111-1-1i3i3−i3−i3i3i3−i3−i300020-20-2021-1−i3i3−i3i3i3−i3-1-1−i3i3i3−i31-11-1−i3i311000000000000
χ522222-2-2-122-2-2-1-1-1-22-22000011-1-11111-1-1i3i3−i3−i3i3i3−i3−i3000-202020-21-1−i3i3−i3i3−i3i311i3−i3−i3i3-11-11i3−i3-1-1000000000000
χ532222-2-2-1-2-222-1-1-12-2-2200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i30020-20-2020-11−i3i3i3−i3-1-1−i3i3-11-11−i3i3i3−i311i3−i3000000000000
χ542222-2-2-1-2-222-1-1-12-2-2200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i300-202020-20-11−i3i3i3−i311i3−i31-11-1i3−i3−i3i3-1-1−i3i3000000000000
χ552222-2-2-1-2-222-1-1-12-2-2200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i30020-20-2020-11i3−i3−i3i3-1-1i3−i3-11-11i3−i3−i3i311−i3i3000000000000
χ562222-2-2-1-2-222-1-1-12-2-2200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i300-202020-20-11i3−i3−i3i311−i3i31-11-1−i3i3i3−i3-1-1i3−i3000000000000
χ572222-2-2-1-2-222-1-1-1-222-200001111-1-1-1-111−i3−i3i3i3i3i3−i3−i3002020-20-201-1i3−i3−i3i3-1-1−i3i31-11-1i3−i3−i3i311i3−i3000000000000
χ582222-2-2-1-2-222-1-1-1-222-200001111-1-1-1-111−i3−i3i3i3i3i3−i3−i300-20-2020201-1i3−i3−i3i311i3−i3-11-11−i3i3i3−i3-1-1−i3i3000000000000
χ592222-2-2-1-2-222-1-1-1-222-200001111-1-1-1-111i3i3−i3−i3−i3−i3i3i3002020-20-201-1−i3i3i3−i3-1-1i3−i31-11-1−i3i3i3−i311−i3i3000000000000
χ602222-2-2-1-2-222-1-1-1-222-200001111-1-1-1-111i3i3−i3−i3−i3−i3i3i300-20-2020201-1−i3i3i3−i311−i3i3-11-11i3−i3−i3i3-1-1i3−i3000000000000
χ612-22-22-222-22-2-2-2200002-22-22-22-22-200002-22-22-22-200000000000000000000000000000000002i−2i002i−2i0000
χ622-22-22-222-22-2-2-2200002-22-22-22-22-200002-22-22-22-20000000000000000000000000000000000−2i2i00−2i2i0000
χ632-22-22-222-22-2-2-220000-22-222-22-22-20000-22-22-22-2200000000000000000000000000000000002i−2i00−2i2i0000
χ642-22-22-222-22-2-2-220000-22-222-22-22-20000-22-22-22-220000000000000000000000000000000000−2i2i002i−2i0000
χ652-22-22-22-22-22-2-2200002-2-222-2-22-2200002-22-2-22-22000000000000000000000000000000002i−2i002i−2i000000
χ662-22-22-22-22-22-2-2200002-2-222-2-22-2200002-22-2-22-2200000000000000000000000000000000−2i2i00−2i2i000000
χ672-22-22-22-22-22-2-220000-222-22-2-22-220000-22-222-22-2000000000000000000000000000000002i−2i00−2i2i000000
χ682-22-22-22-22-22-2-220000-222-22-2-22-220000-22-222-22-200000000000000000000000000000000−2i2i002i−2i000000
χ694-44-44-4-24-44-422-200004-44-4-22-22-220000-22-22-22-2200000000000000000000000000000000000000000000
χ704-44-44-4-24-44-422-20000-44-44-22-22-2200002-22-22-22-200000000000000000000000000000000000000000000
χ714-44-44-4-2-44-4422-200004-4-44-222-22-20000-22-222-22-200000000000000000000000000000000000000000000
χ724-44-44-4-2-44-4422-20000-444-4-222-22-200002-22-2-22-2200000000000000000000000000000000000000000000
χ734-44-4-4444-4-44-4-4400000000-444-4-4400000000000000000000000000000000000000000000000000000000
χ744-44-4-444-444-4-4-4400000000-44-444-400000000000000000000000000000000000000000000000000000000
χ754-44-4-44-24-4-4422-2000000002-2-222-20000−2i32i32i3−2i3−2i32i32i3−2i300000000000000000000000000000000000000000000
χ764-44-4-44-24-4-4422-2000000002-2-222-200002i3−2i3−2i32i32i3−2i3−2i32i300000000000000000000000000000000000000000000
χ774-44-4-44-2-444-422-2000000002-22-2-220000−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000
χ784-44-4-44-2-444-422-2000000002-22-2-2200002i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000
χ7988-8-800800008-8-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-40000-444000000000000000043−430000000000000000000000000000000000000000000000000000
χ8188-8-800-40000-4440000000000000000−43430000000000000000000000000000000000000000000000000000
χ828-8-880080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-400004-440000000000000043−43000000000000000000000000000000000000000000000000000000
χ848-8-8800-400004-4400000000000000−4343000000000000000000000000000000000000000000000000000000

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