Finite Group Databasebeta

← Group #10702889

Character table — Group #10702889

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222222222222222236666666666666666666224444444444666612121212121212121212121212121212121212124444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-11ii−i−i−i−iii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-11ii−i−i−i−iii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-11−i−iiiii−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-11−i−iiiii−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ18222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ19222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ20222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ21222222222-2-2-2-2-2-22-2-2-1-1-1-11111-1-1-1-1-1-11111112-22-22i2i−2i−2i2i2i−2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ22222222222-2-2-2-2-2-22-2-2-1-1-1-11111-1-1-1-1-1-11111112-22-2−2i−2i2i2i−2i−2i2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ23222222222-2-2-2-2-2-22-2-2-1-1-1-11111-1-1-1-1-1-1111111-22-222i2i−2i−2i−2i−2i2i2i11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ24222222222-2-2-2-2-2-22-2-2-1-1-1-11111-1-1-1-1-1-1111111-22-22−2i−2i2i2i2i2i−2i−2i11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ25222222-2-2-2222-2-2-2-22-22222-2-2-2-222-2-2-2-22222-2-2000000002i−2i2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ26222222-2-2-2222-2-2-2-22-22222-2-2-2-222-2-2-2-22222-2-200000000−2i2i−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ27222222-2-2-2222-2-2-2-22-2-1-1-1-11111-1-11111-1-1-1-111000000002i−2i2i−2i−i3i3−i3i3−i3i3−i3i333−3−333−3−3−i−iii−i−iii0000000000000000
χ28222222-2-2-2222-2-2-2-22-2-1-1-1-11111-1-11111-1-1-1-111000000002i−2i2i−2ii3−i3i3−i3i3−i3i3−i3−3−333−3−333−i−iii−i−iii0000000000000000
χ29222222-2-2-2222-2-2-2-22-2-1-1-1-11111-1-11111-1-1-1-11100000000−2i2i−2i2i−i3i3−i3i3−i3i3−i3i3−3−333−3−333ii−i−iii−i−i0000000000000000
χ30222222-2-2-2222-2-2-2-22-2-1-1-1-11111-1-11111-1-1-1-11100000000−2i2i−2i2ii3−i3i3−i3i3−i3i3−i333−3−333−3−3ii−i−iii−i−i0000000000000000
χ31222222-2-2-2-2-2-2222-2-222222222222-2-2-2-2-2-2-2-222000000002-2-22000000000000000022-2-2-2-2220000000000000000
χ32222222-2-2-2-2-2-2222-2-222222222222-2-2-2-2-2-2-2-22200000000-222-20000000000000000-2-22222-2-20000000000000000
χ33222222-2-2-2-2-2-2222-2-22-1-1-1-1-1-1-1-1-1-111111111-1-1000000002-2-22−i3i3i3−i3−i3i3i3−i3−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000000000
χ34222222-2-2-2-2-2-2222-2-22-1-1-1-1-1-1-1-1-1-111111111-1-1000000002-2-22i3−i3−i3i3i3−i3−i3i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000000000
χ35222222-2-2-2-2-2-2222-2-22-1-1-1-1-1-1-1-1-1-111111111-1-100000000-222-2−i3i3i3−i3−i3i3i3−i3i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000000000
χ36222222-2-2-2-2-2-2222-2-22-1-1-1-1-1-1-1-1-1-111111111-1-100000000-222-2i3−i3−i3i3i3−i3−i3i3−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000000000
χ372222-2-222-222-22-2-2-2-222222-2-2-2-2-2-222-2-222-2-22200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ382222-2-222-222-22-2-2-2-222222-2-2-2-2-2-222-2-222-2-2220000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ392222-2-222-222-22-2-2-2-22-1-1-1-1111111-1-111-1-111-1-100002i−2i2i−2i0000−i3i3−i3i3i3−i3i3−i3−ii−ii−ii−ii3−33−33−33−30000000000000000
χ402222-2-222-222-22-2-2-2-22-1-1-1-1111111-1-111-1-111-1-100002i−2i2i−2i0000i3−i3i3−i3−i3i3−i3i3−ii−ii−ii−ii−33−33−33−330000000000000000
χ412222-2-222-222-22-2-2-2-22-1-1-1-1111111-1-111-1-111-1-10000−2i2i−2i2i0000−i3i3−i3i3i3−i3i3−i3i−ii−ii−ii−i−33−33−33−330000000000000000
χ422222-2-222-222-22-2-2-2-22-1-1-1-1111111-1-111-1-111-1-10000−2i2i−2i2i0000i3−i3i3−i3−i3i3−i3i3i−ii−ii−ii−i3−33−33−33−30000000000000000
χ432222-2-222-2-2-22-222-22-222222222-2-222-2-2-2-222-2-200002-2-220000000000002-22-2-22-22000000000000000000000000
χ442222-2-222-2-2-22-222-22-222222222-2-222-2-2-2-222-2-20000-222-2000000000000-22-222-22-2000000000000000000000000
χ452222-2-222-2-2-22-222-22-2-1-1-1-1-1-1-1-111-1-11111-1-11100002-2-220000−i3i3i3−i3i3−i3−i3i3-11-111-11-1−i3i3−i3i3i3−i3i3−i30000000000000000
χ462222-2-222-2-2-22-222-22-2-1-1-1-1-1-1-1-111-1-11111-1-11100002-2-220000i3−i3−i3i3−i3i3i3−i3-11-111-11-1i3−i3i3−i3−i3i3−i3i30000000000000000
χ472222-2-222-2-2-22-222-22-2-1-1-1-1-1-1-1-111-1-11111-1-1110000-222-20000−i3i3i3−i3i3−i3−i3i31-11-1-11-11i3−i3i3−i3−i3i3−i3i30000000000000000
χ482222-2-222-2-2-22-222-22-2-1-1-1-1-1-1-1-111-1-11111-1-1110000-222-20000i3−i3−i3i3−i3i3i3−i31-11-1-11-11−i3i3−i3i3i3−i3i3−i30000000000000000
χ492222-2-2-2-2222-2-2222-2-222222222-2-2-2-22222-2-2-2-222-2-2000000002222-2-2-2-200000000000000000000000000000000
χ502222-2-2-2-2222-2-2222-2-222222222-2-2-2-22222-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000000000
χ512222-2-2-2-2222-2-2222-2-2-1-1-1-1-1-1-1-11111-1-1-1-1111122-2-200000000-1-1-1-11111−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ522222-2-2-2-2222-2-2222-2-2-1-1-1-1-1-1-1-11111-1-1-1-1111122-2-200000000-1-1-1-11111i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ532222-2-2-2-2222-2-2222-2-2-1-1-1-1-1-1-1-11111-1-1-1-11111-2-222000000001111-1-1-1-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ542222-2-2-2-2222-2-2222-2-2-1-1-1-1-1-1-1-11111-1-1-1-11111-2-222000000001111-1-1-1-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ552222-2-2-2-22-2-222-2-22222222-2-2-2-2-2-2-2-222-2-222222-2-220000000022-2-2-2-22200000000000000000000000000000000
χ562222-2-2-2-22-2-222-2-22222222-2-2-2-2-2-2-2-222-2-22222-222-200000000-2-22222-2-200000000000000000000000000000000
χ572222-2-2-2-22-2-222-2-2222-1-1-1-111111111-1-111-1-1-1-12-2-2200000000-1-11111-1-13−3−33−333−33−3−33−333−30000000000000000
χ582222-2-2-2-22-2-222-2-2222-1-1-1-111111111-1-111-1-1-1-12-2-2200000000-1-11111-1-1−333−33−3−33−333−33−3−330000000000000000
χ592222-2-2-2-22-2-222-2-2222-1-1-1-111111111-1-111-1-1-1-1-222-20000000011-1-1-1-1113−3−33−333−3−333−33−3−330000000000000000
χ602222-2-2-2-22-2-222-2-2222-1-1-1-111111111-1-111-1-1-1-1-222-20000000011-1-1-1-111−333−33−3−333−3−33−333−30000000000000000
χ6122-2-22-22-222-22-22-2-2-222-2-2222-2-22-22-22-22-22-22-20000000000000000000000000000000000002i−2i2i−2i000000000000
χ6222-2-22-22-222-22-22-2-2-222-2-2222-2-22-22-22-22-22-22-2000000000000000000000000000000000000−2i2i−2i2i000000000000
χ6322-2-22-22-22-22-22-22-22-22-2-22-2-2222-22-22-2-22-22-220000000000000000000000000000000000002i−2i−2i2i000000000000
χ6422-2-22-22-22-22-22-22-22-22-2-22-2-2222-22-22-2-22-22-22000000000000000000000000000000000000−2i2i2i−2i000000000000
χ6522-2-22-2-22-22-222-222-2-22-2-22-2-2222-2-22-222-22-2-220000000000000000000000000000000000000000000000002i−2i2i−2i
χ6622-2-22-2-22-22-222-222-2-22-2-22-2-2222-2-22-222-22-2-22000000000000000000000000000000000000000000000000−2i2i−2i2i
χ6722-2-22-2-22-2-22-2-22-22222-2-2222-2-22-2-22-22-22-222-20000000000000000000000000000000000000000000000002-2-22
χ6822-2-22-2-22-2-22-2-22-22222-2-2222-2-22-2-22-22-22-222-2000000000000000000000000000000000000000000000000-222-2
χ6922-2-2-222-2-22-2-2-2-222222-2-22-2-222-222-2-222-2-222-2000000000000000000000000000000000000000000002-22-20000
χ7022-2-2-222-2-22-2-2-2-222222-2-22-2-222-222-2-222-2-222-200000000000000000000000000000000000000000000-22-220000
χ7122-2-2-222-2-2-22222-22-2-22-2-2222-2-2-222-2-22-222-2-22000000000000000000000000000000000000000000002i−2i−2i2i0000
χ7222-2-2-222-2-2-22222-22-2-22-2-2222-2-2-222-2-22-222-2-2200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ7322-2-2-22-2222-2-222-2-22-22-2-2222-2-2-22-222-22-2-22-2200000000000000000000000000000000000000002i−2i2i−2i00000000
χ7422-2-2-22-2222-2-222-2-22-22-2-2222-2-2-22-222-22-2-22-220000000000000000000000000000000000000000−2i2i−2i2i00000000
χ7522-2-2-22-222-222-2-22-2-222-2-22-2-222-22-222-2-222-22-200000000000000000000000000000000000000002i−2i−2i2i00000000
χ7622-2-2-22-222-222-2-22-2-222-2-22-2-222-22-222-2-222-22-20000000000000000000000000000000000000000−2i2i2i−2i00000000
χ7744-4-44-44-444-44-44-4-4-44-222-2-2-222-22-22-22-22-22-220000000000000000000000000000000000000000000000000000
χ7844-4-44-44-44-44-44-44-44-4-222-222-2-2-22-22-222-22-22-20000000000000000000000000000000000000000000000000000
χ7944-4-44-4-44-44-444-444-4-4-222-222-2-2-222-22-2-22-222-20000000000000000000000000000000000000000000000000000
χ8044-4-44-4-44-4-44-4-44-4444-222-2-2-222-222-22-22-22-2-220000000000000000000000000000000000000000000000000000
χ8144-4-4-444-4-44-4-4-4-44444-222-222-2-22-2-222-2-222-2-220000000000000000000000000000000000000000000000000000
χ8244-4-4-444-4-4-44444-44-4-4-222-2-2-2222-2-222-22-2-222-20000000000000000000000000000000000000000000000000000
χ8344-4-4-44-4444-4-444-4-44-4-222-2-2-2222-22-2-22-222-22-20000000000000000000000000000000000000000000000000000
χ8444-4-4-44-444-444-4-44-4-44-222-222-2-22-22-2-222-2-22-220000000000000000000000000000000000000000000000000000
χ858-88-80000000000000088-8-800000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800000000000000-4-444−4i34i3−4i34i30000000000000000000000000000000000000000000000000000000000000000
χ878-88-800000000000000-4-4444i3−4i34i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000000000008-88-800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-8800000000000000-44-44−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ908-8-8800000000000000-44-444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000

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