Finite Group Databasebeta

← Group #10828645

Character table — Group #10828645

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222224444444444444444444444444488888888888888888888888888888888242424242424242448484848
order122222344446662244444466666612121212121212121212121222444444446666121212121212121212121212121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-11-1-1-11-111-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-11-1-1-11-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-11-1-1-11-1-111-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-11-1-1-11-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ911111111111111-1-1-1-1111111-1-1-1-11111111111111-11-1-11-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-11-11-1
χ1011111111111111-1-1-1-1111111-1-1-1-11111111111111-11-1-11-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-111-11-11
χ1111111111111111-1-1-1-1111111-1-1-1-1111111111111-11-111-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1-11-11
χ1211111111111111-1-1-1-1111111-1-1-1-1111111111111-11-111-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1111-11-1
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-111-1
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-11-1-11
χ172222222-2-2-2-222222-2-222-2-2222222-2-2-2-22222-2-2-2-20000002-20000000000-2-2000022-2-20000000000000000
χ182222222-2-2-2-222222-2-2-2-222222222-2-2-2-2-2-2-2-22222000000-220000000000-2-20000-2-2220000000000000000
χ192222222-2-2-2-2222-2-22222-2-222-2-2-2-2-2-2-2-22222-2-2-2-2000000-220000000000220000-2-2220000000000000000
χ202222222-2-2-2-2222-2-222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222220000002-2000000000022000022-2-20000000000000000
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
χ22222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-211111111-1-11111-1-1-1-11111000000000000
χ23222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111112-22-22-2-2-22-2-1-111-1-111-1-1-1-1111111-1-111000000000000
χ24222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-22-22-22-2-2-2211-1-111-1-1-1-111-1-1111111-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-22222-1-11111-1-1-1-1-1-1-1-1-1-1-1-12-22-2-22-2-2-22-1-11111-1-111-1-111111111-1-1000000000000
χ26222222-12222-1-1-1-2-2-2-22222-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-22-222-2-2-22-211-1-1-1-1111111-1-11111-1-111000000000000
χ27222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-1111111112222-2-222-2-2-1-1-1-1111111-1-1-1-1-1-1-1-11111000000000000
χ28222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-111111111-2-2-2-22222221111-1-1-1-1111111-1-1-1-1-1-1-1-1000000000000
χ29222222-1-2-2-2-2-1-1-122-2-222-2-2-1-1-1-1-1-11111-1-1-1-111110000002-200−i3i3−i3i3−i3i3−i3i311−i3i3−i3i3-1-111−i3i3−i3i3000000000000
χ30222222-1-2-2-2-2-1-1-122-2-222-2-2-1-1-1-1-1-11111-1-1-1-111110000002-200i3−i3i3−i3i3−i3i3−i311i3−i3i3−i3-1-111i3−i3i3−i3000000000000
χ31222222-1-2-2-2-2-1-1-122-2-2-2-222-1-1-1-1-1-111111111-1-1-1-1000000-2200−i3i3i3−i3−i3i3i3−i311−i3i3i3−i311-1-1−i3i3i3−i3000000000000
χ32222222-1-2-2-2-2-1-1-122-2-2-2-222-1-1-1-1-1-111111111-1-1-1-1000000-2200i3−i3−i3i3i3−i3−i3i311i3−i3−i3i311-1-1i3−i3−i3i3000000000000
χ33222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-111111111-1-1-1-11111000000-2200−i3i3i3−i3i3−i3−i3i3-1-1−i3i3i3−i311-1-1i3−i3−i3i3000000000000
χ34222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-111111111-1-1-1-11111000000-2200i3−i3−i3i3−i3i3i3−i3-1-1i3−i3−i3i311-1-1−i3i3i3−i3000000000000
χ35222222-1-2-2-2-2-1-1-1-2-222-2-222-1-1111111111111-1-1-1-10000002-200−i3i3−i3i3i3−i3i3−i3-1-1−i3i3−i3i3-1-111i3−i3i3−i3000000000000
χ36222222-1-2-2-2-2-1-1-1-2-222-2-222-1-1111111111111-1-1-1-10000002-200i3−i3i3−i3−i3i3−i3i3-1-1i3−i3i3−i3-1-111−i3i3−i3i3000000000000
χ372222-2-2222-2-22222-22-20000-2-222-2-222-2-200000000020-202000-2002200222-200-2-2000000-2-2000000000000
χ382222-2-2222-2-22222-22-20000-2-222-2-222-2-2000000000-2020-2000200-2-200-2-22-2002200000022000000000000
χ392222-2-2222-2-2222-22-220000-2-2-2-22222-2-200000000020-20-20002002200-2-2-2200-2-200000022000000000000
χ402222-2-2222-2-2222-22-220000-2-2-2-22222-2-2000000000-20202000-200-2-20022-220022000000-2-2000000000000
χ412222-2-22-2-2222222-2-220000-2-222-2-2-2-2220000000020-202000-2022002200-22-2-2000000-2-200000000000000
χ422222-2-22-2-2222222-2-220000-2-222-2-2-2-22200000000-2020-200020-2-200-2-200-22220000002200000000000000
χ432222-2-22-2-222222-222-20000-2-2-2-222-2-2220000000020-20-2000202200-2-2002-2-2-20000002200000000000000
χ442222-2-22-2-222222-222-20000-2-2-2-222-2-22200000000-20202000-20-2-20022002-222000000-2-200000000000000
χ452222-2-2-122-2-2-1-1-12-22-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i3020-202000-2−i3i3-1-1−i3i3-1-1-11i3−i311−i3i3−i3i3i3−i311000000000000
χ462222-2-2-122-2-2-1-1-12-22-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i30-2020-20002i3−i311i3−i311-11−i3i3-1-1−i3i3−i3i3−i3i3-1-1000000000000
χ472222-2-2-122-2-2-1-1-12-22-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i3020-202000-2i3−i3-1-1i3−i3-1-1-11−i3i311i3−i3i3−i3−i3i311000000000000
χ482222-2-2-122-2-2-1-1-12-22-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i30-2020-20002−i3i311−i3i311-11i3−i3-1-1i3−i3i3−i3i3−i3-1-1000000000000
χ492222-2-2-122-2-2-1-1-1-22-2200001111-1-1-1-111−i3−i3i3i3−i3−i3i3i3020-20-20002i3−i3-1-1−i3i3111-1−i3i311i3−i3i3−i3i3−i3-1-1000000000000
χ502222-2-2-122-2-2-1-1-1-22-2200001111-1-1-1-111−i3−i3i3i3−i3−i3i3i30-20202000-2−i3i311i3−i3-1-11-1i3−i3-1-1i3−i3i3−i3−i3i311000000000000
χ512222-2-2-122-2-2-1-1-1-22-2200001111-1-1-1-111i3i3−i3−i3i3i3−i3−i3020-20-20002−i3i3-1-1i3−i3111-1i3−i311−i3i3−i3i3−i3i3-1-1000000000000
χ522222-2-2-122-2-2-1-1-1-22-2200001111-1-1-1-111i3i3−i3−i3i3i3−i3−i30-20202000-2i3−i311−i3i3-1-11-1−i3i3-1-1−i3i3−i3i3i3−i311000000000000
χ532222-2-2-1-2-222-1-1-12-2-22000011-1-11111-1-1−i3−i3i3i3i3i3−i3−i320-202000-20-1-1−i3i3-1-1−i3i31-111i3−i3−i3i3i3−i311i3−i3000000000000
χ542222-2-2-1-2-222-1-1-12-2-22000011-1-11111-1-1−i3−i3i3i3i3i3−i3−i3-2020-20002011i3−i311i3−i31-1-1-1−i3i3−i3i3i3−i3-1-1−i3i3000000000000
χ552222-2-2-1-2-222-1-1-12-2-22000011-1-11111-1-1i3i3−i3−i3−i3−i3i3i320-202000-20-1-1i3−i3-1-1i3−i31-111−i3i3i3−i3−i3i311−i3i3000000000000
χ562222-2-2-1-2-222-1-1-12-2-22000011-1-11111-1-1i3i3−i3−i3−i3−i3i3i3-2020-20002011−i3i311−i3i31-1-1-1i3−i3i3−i3−i3i3-1-1i3−i3000000000000
χ572222-2-2-1-2-222-1-1-1-222-200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i320-20-200020-1-1i3−i311−i3i3-1111−i3i3i3−i3−i3i3-1-1i3−i3000000000000
χ582222-2-2-1-2-222-1-1-1-222-200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i3-20202000-2011−i3i3-1-1i3−i3-11-1-1i3−i3i3−i3−i3i311−i3i3000000000000
χ592222-2-2-1-2-222-1-1-1-222-200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i320-20-200020-1-1−i3i311i3−i3-1111i3−i3−i3i3i3−i3-1-1−i3i3000000000000
χ602222-2-2-1-2-222-1-1-1-222-200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i3-20202000-2011i3−i3-1-1−i3i3-11-1-1−i3i3−i3i3i3−i311i3−i3000000000000
χ6122-2-2-2222-22-2-22-200002i−2i2i−2i2-200002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000002i−2i002-20000
χ6222-2-2-2222-22-2-22-200002i−2i2i−2i2-200002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−2i2i00-220000
χ6322-2-2-2222-22-2-22-20000−2i2i−2i2i2-200002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000002i−2i00-220000
χ6422-2-2-2222-22-2-22-20000−2i2i−2i2i2-200002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−2i2i002-20000
χ6522-2-2-222-22-22-22-200002i−2i−2i2i2-20000-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000002i−2i002-2000000
χ6622-2-2-222-22-22-22-200002i−2i−2i2i2-20000-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000−2i2i00-22000000
χ6722-2-2-222-22-22-22-20000−2i2i2i−2i2-20000-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000002i−2i00-22000000
χ6822-2-2-222-22-22-22-20000−2i2i2i−2i2-20000-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000−2i2i002-2000000
χ6944-4-44-444-4-44-44-400000000-4400004-4-440000000000000000000000000000000000000000000000000000
χ7044-4-44-44-444-4-44-400000000-440000-444-40000000000000000000000000000000000000000000000000000
χ7144-4-44-4-24-4-442-22000000002-20000-222-223−23−232323−23−232300000000000000000000000000000000000000000000
χ7244-4-44-4-24-4-442-22000000002-20000-222-2−232323−23−232323−2300000000000000000000000000000000000000000000
χ7344-4-44-4-2-444-42-22000000002-200002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000
χ7444-4-44-4-2-444-42-22000000002-200002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000
χ7544-4-4-44-24-44-42-2200004i−4i4i−4i-220000-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000
χ7644-4-4-44-24-44-42-220000−4i4i−4i4i-220000-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ7744-4-4-44-2-44-442-2200004i−4i−4i4i-2200002-22-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ7844-4-4-44-2-44-442-220000−4i4i4i−4i-2200002-22-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000
χ798-88-800800008-8-80000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-40000-4440000000000−4i34i30000000000000000000000000000000000000000000000000000000000
χ818-88-800-40000-44400000000004i3−4i30000000000000000000000000000000000000000000000000000000000
χ828-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-4000044-4000000000000−4i34i300000000000000000000000000000000000000000000000000000000
χ848-8-8800-4000044-40000000000004i3−4i300000000000000000000000000000000000000000000000000000000

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