Finite Group Databasebeta

← Group #10830412

Character table — Group #10830412

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222224444444444444444444444444488888888888888888888888888888888242424242424242448484848
order1222223444466622224444666666666612121212121212122222444444666666661212121212121212121212121212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ7111111111111111111-1-1-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ8111111111111111111-1-1-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ911111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-11-1-1-11-11-111-1-111-1-111-1-1-1-111-1-111-1-11111-1-1-1-11-11-1
χ1011111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-11-1-1-11-11-111-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-11-11
χ1111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-11-11-1-1-11-11-1-111-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-11-11
χ1211111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-11-11-1-1-11-11-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-111111-11-1
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1111-1-1-1-111-1-1111111-1-1-1-111-1-11111-1-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-111-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-111-111-1
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-111-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-11-1-11
χ172222222-2-2-2-222222-2-222-2-2222222-2-2-2-22222-2-2-2-200002-2000000000000-2-222-2-200000000000000000000
χ182222222-2-2-2-222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2200000000000022-2-22200000000000000000000
χ192222222-2-2-2-2222-2-22222-2-222-2-2-2-222222222-2-2-2-20000-22000000000000-2-2-2-22200000000000000000000
χ202222222-2-2-2-2222-2-222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-200002-20000000000002222-2-200000000000000000000
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
χ22222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-211111111-1-1-1-1-1-111111111000000000000
χ23222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111-1-1-1-122-2-2-2-222-2-2-1-1-1-11111111111-1-1-1-11111000000000000
χ24222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-2-222-2-2-2-2221111-1-1-1-11111111111-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-12-22-2-2-22-22-2-1-111-1-111-1-11111-1-111-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-22-22-2-2-22-2211-1-111-1-1-1-1111111-1-111-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111-1-1-1-12-2-22222-2-22-1-11111-1-111-1-1-1-1-1-11111-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111-1-1-1-1-222-222-222-211-1-1-1-11111-1-1-1-111-1-1-1-111000000000000
χ29222222-1-2-2-2-2-1-1-122-2-222-2-2-1-1-1-1-1-11111-1-1-1-1111100002-20000−i3i3−i3i3−i3i3−i3i311-1-111−i3i3−i3i3−i3i3−i3i3000000000000
χ30222222-1-2-2-2-2-1-1-122-2-222-2-2-1-1-1-1-1-11111-1-1-1-1111100002-20000i3−i3i3−i3i3−i3i3−i311-1-111i3−i3i3−i3i3−i3i3−i3000000000000
χ31222222-1-2-2-2-2-1-1-122-2-2-2-222-1-1-1-1-1-11111111111110000-220000−i3i3−i3i3i3−i3i3−i3-1-111-1-1−i3i3−i3i3i3−i3i3−i3000000000000
χ32222222-1-2-2-2-2-1-1-122-2-2-2-222-1-1-1-1-1-11111111111110000-220000i3−i3i3−i3−i3i3−i3i3-1-111-1-1i3−i3i3−i3−i3i3−i3i3000000000000
χ33222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-11111-1-1-1-1-1-1-1-111110000-220000−i3i3i3−i3−i3i3i3−i31111-1-1−i3i3i3−i3−i3i3i3−i3000000000000
χ34222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-11111-1-1-1-1-1-1-1-111110000-220000i3−i3−i3i3i3−i3−i3i31111-1-1i3−i3−i3i3i3−i3−i3i3000000000000
χ35222222-1-2-2-2-2-1-1-1-2-222-2-222-1-11111-1-1-1-11111111100002-20000−i3i3i3−i3i3−i3−i3i3-1-1-1-111−i3i3i3−i3i3−i3−i3i3000000000000
χ36222222-1-2-2-2-2-1-1-1-2-222-2-222-1-11111-1-1-1-11111111100002-20000i3−i3−i3i3−i3i3i3−i3-1-1-1-111i3−i3−i3i3−i3i3i3−i3000000000000
χ372222-2-222-22-222200002-22-2-2-20000000022-2-222-2-20202000-20-2002200222-2000000-2-200-2-2000000000000
χ382222-2-222-22-222200002-22-2-2-20000000022-2-222-2-20-20-200020200-2-200-2-22-2000000220022000000000000
χ392222-2-222-22-22220000-22-22-2-200000000-2-22222-2-2020-2000-202002200-2-2-22000000-2-20022000000000000
χ402222-2-222-22-22220000-22-22-2-200000000-2-22222-2-20-20200020-200-2-20022-220000002200-2-2000000000000
χ412222-2-22-22-2222200002-2-22-2-20000000022-2-2-2-222202000-20-2022002200-220000-2-200-2-200000000000000
χ422222-2-22-22-2222200002-2-22-2-20000000022-2-2-2-222-20-20002020-2-200-2-200-22000022002200000000000000
χ432222-2-22-22-222220000-222-2-2-200000000-2-222-2-22220-2000-20202200-2-2002-20000-2-2002200000000000000
χ442222-2-22-22-222220000-222-2-2-200000000-2-222-2-222-20200020-20-2-20022002-200002200-2-200000000000000
χ452222-2-2-12-22-2-1-1-100002-22-211−i3−i3i3i3−i3−i3i3i3-1-111-1-1110202000-20-2−i3i3-1-1−i3i3-1-1-11−i3i3−i3i3i3−i311i3−i311000000000000
χ462222-2-2-12-22-2-1-1-100002-22-211−i3−i3i3i3−i3−i3i3i3-1-111-1-1110-20-2000202i3−i311i3−i311-11−i3i3−i3i3−i3i3-1-1−i3i3-1-1000000000000
χ472222-2-2-12-22-2-1-1-100002-22-211i3i3−i3−i3i3i3−i3−i3-1-111-1-1110202000-20-2i3−i3-1-1i3−i3-1-1-11i3−i3i3−i3−i3i311−i3i311000000000000
χ482222-2-2-12-22-2-1-1-100002-22-211i3i3−i3−i3i3i3−i3−i3-1-111-1-1110-20-2000202−i3i311−i3i311-11i3−i3i3−i3i3−i3-1-1i3−i3-1-1000000000000
χ492222-2-2-12-22-2-1-1-10000-22-2211−i3−i3i3i3−i3−i3i3i311-1-1-1-111020-2000-202−i3i3-1-1i3−i3111-1i3−i3i3−i3i3−i311−i3i3-1-1000000000000
χ502222-2-2-12-22-2-1-1-10000-22-2211−i3−i3i3i3−i3−i3i3i311-1-1-1-1110-20200020-2i3−i311−i3i3-1-11-1i3−i3i3−i3−i3i3-1-1i3−i311000000000000
χ512222-2-2-12-22-2-1-1-10000-22-2211i3i3−i3−i3i3i3−i3−i311-1-1-1-111020-2000-202i3−i3-1-1−i3i3111-1−i3i3−i3i3−i3i311i3−i3-1-1000000000000
χ522222-2-2-12-22-2-1-1-10000-22-2211i3i3−i3−i3i3i3−i3−i311-1-1-1-1110-20200020-2−i3i311i3−i3-1-11-1−i3i3−i3i3i3−i3-1-1−i3i311000000000000
χ532222-2-2-1-22-22-1-1-100002-2-2211−i3−i3i3i3i3i3−i3−i3-1-11111-1-1202000-20-20-1-1−i3i3-1-1−i3i31-1−i3i3i3−i311i3−i311i3−i3000000000000
χ542222-2-2-1-22-22-1-1-100002-2-2211−i3−i3i3i3i3i3−i3−i3-1-11111-1-1-20-2000202011i3−i311i3−i31-1−i3i3i3−i3-1-1−i3i3-1-1−i3i3000000000000
χ552222-2-2-1-22-22-1-1-100002-2-2211i3i3−i3−i3−i3−i3i3i3-1-11111-1-1202000-20-20-1-1i3−i3-1-1i3−i31-1i3−i3−i3i311−i3i311−i3i3000000000000
χ562222-2-2-1-22-22-1-1-100002-2-2211i3i3−i3−i3−i3−i3i3i3-1-11111-1-1-20-2000202011−i3i311−i3i31-1i3−i3−i3i3-1-1i3−i3-1-1i3−i3000000000000
χ572222-2-2-1-22-22-1-1-10000-222-211−i3−i3i3i3i3i3−i3−i311-1-111-1-120-2000-2020-1-1−i3i311i3−i3-11i3−i3−i3i311i3−i3-1-1−i3i3000000000000
χ582222-2-2-1-22-22-1-1-10000-222-211−i3−i3i3i3i3i3−i3−i311-1-111-1-1-20200020-2011i3−i3-1-1−i3i3-11i3−i3−i3i3-1-1−i3i311i3−i3000000000000
χ592222-2-2-1-22-22-1-1-10000-222-211i3i3−i3−i3−i3−i3i3i311-1-111-1-120-2000-2020-1-1i3−i311−i3i3-11−i3i3i3−i311−i3i3-1-1i3−i3000000000000
χ602222-2-2-1-22-22-1-1-10000-222-211i3i3−i3−i3−i3−i3i3i311-1-111-1-1-20200020-2011−i3i3-1-1i3−i3-11−i3i3i3−i3-1-1i3−i311−i3i3000000000000
χ612-22-22-2222-2-2-2-222-22-200002-22-22-22-22-200002-22-200000000000000000000000000000000002i−2i002i−2i0000
χ622-22-22-2222-2-2-2-222-22-200002-22-22-22-22-200002-22-20000000000000000000000000000000000−2i2i00−2i2i0000
χ632-22-22-2222-2-2-2-22-22-2200002-2-22-22-22-2200002-22-200000000000000000000000000000000002i−2i00−2i2i0000
χ642-22-22-2222-2-2-2-22-22-2200002-2-22-22-22-2200002-22-20000000000000000000000000000000000−2i2i002i−2i0000
χ652-22-22-22-2-222-2-222-2-2200002-22-22-2-22-220000-22-22000000000000000000000000000000002-2002-2000000
χ662-22-22-22-2-222-2-222-2-2200002-22-22-2-22-220000-22-2200000000000000000000000000000000-2200-22000000
χ672-22-22-22-2-222-2-22-222-200002-2-22-222-22-20000-22-22000000000000000000000000000000002-200-22000000
χ682-22-22-22-2-222-2-22-222-200002-2-22-222-22-20000-22-2200000000000000000000000000000000-22002-2000000
χ694-44-44-4-244-4-422-24-44-40000-22-22-22-22-220000-22-2200000000000000000000000000000000000000000000
χ704-44-44-4-244-4-422-2-44-440000-222-22-22-22-20000-22-2200000000000000000000000000000000000000000000
χ714-44-44-4-2-4-44422-24-4-440000-22-22-222-22-200002-22-200000000000000000000000000000000000000000000
χ724-44-44-4-2-4-44422-2-444-40000-222-22-2-22-2200002-22-200000000000000000000000000000000000000000000
χ734-44-4-4444-4-44-4-4400000000-440000000000004-4-4400000000000000000000000000000000000000000000
χ744-44-4-444-444-4-4-4400000000-44000000000000-444-400000000000000000000000000000000000000000000
χ754-44-4-44-24-4-4422-2000000002-2−2i32i32i3−2i3−2i32i32i3−2i30000-222-200000000000000000000000000000000000000000000
χ764-44-4-44-24-4-4422-2000000002-22i3−2i3−2i32i32i3−2i3−2i32i30000-222-200000000000000000000000000000000000000000000
χ774-44-4-44-2-444-422-2000000002-2−2i32i32i3−2i32i3−2i3−2i32i300002-2-2200000000000000000000000000000000000000000000
χ784-44-4-44-2-444-422-2000000002-22i3−2i3−2i32i3−2i32i32i3−2i300002-2-2200000000000000000000000000000000000000000000
χ7988-8-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-400004-44000000000000000000−4i34i300000000000000000000000000000000000000000000000000
χ8188-8-800-400004-440000000000000000004i3−4i300000000000000000000000000000000000000000000000000
χ828-8-8800800008-8-80000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-40000-4440000000000000000000043−43000000000000000000000000000000000000000000000000
χ848-8-8800-40000-44400000000000000000000−4343000000000000000000000000000000000000000000000000

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