Finite Group Databasebeta

← Group #10702927

Character table — Group #10702927

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1244222222234444444666121212126666661212121212128888888888882424242424242424242424242424242424242424242424242244444444448888
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
χ9111111-1-1-11-1111-11-1-1-1111111111-1-1-1-11-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1ii−i−iii−i−i
χ10111111-1-1-11-1111-11-1-1-1111111111-1-1-1-11-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−i−iii−i−iii
χ11111111-1-1-11-1111-11-1-1-1111111111-1-1-1-11-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−i−iii−i−iii
χ12111111-1-1-11-1111-11-1-1-1111111111-1-1-1-11-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111ii−i−iii−i−i
χ13111111-1-1-11-1111-11-1-1-1111111111-1-1-1-11-1-11-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111ii−i−i−i−iii
χ14111111-1-1-11-1111-11-1-1-1111111111-1-1-1-11-1-11-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1−i−iiiii−i−i
χ15111111-1-1-11-1111-11-1-1-1111111111-1-1-1-11-1-11-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111−i−iiiii−i−i
χ16111111-1-1-11-1111-11-1-1-1111111111-1-1-1-11-1-11-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1ii−i−i−i−iii
χ1722222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ1922222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ2022222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ21222222-2-2-22-2-122-22-2-2-2-1-1-1-1-1-1-1-1-11111-111-11122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ22222222-2-2-22-2-122-22-2-2-2-1-1-1-1-1-1-1-1-11111-111-11122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ23222222-2-2-22-2-122-22-2-2-2-1-1-1-1-1-1-1-1-11111-111-111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ24222222-2-2-22-2-122-22-2-2-2-1-1-1-1-1-1-1-1-11111-111-111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ2522222-222-2-2-222-2-2-22-222222222-2-222-2-2-22-2-22-22i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ2622222-222-2-2-222-2-2-22-222222222-2-222-2-2-22-2-22-2−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ2722222-222-2-2-2-12-2-2-22-22-1-1-1-1-1-1-111-1-1111-111-112i−2i2i−2i00000000−i−iii−i−iii−i3−i3i3i3−i3−i3i3i333−3−333−3−30000000000000000
χ2822222-222-2-2-2-12-2-2-22-22-1-1-1-1-1-1-111-1-1111-111-112i−2i2i−2i00000000−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3−3−333−3−3330000000000000000
χ2922222-222-2-2-2-12-2-2-22-22-1-1-1-1-1-1-111-1-1111-111-11−2i2i−2i2i00000000ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i3−3−333−3−3330000000000000000
χ3022222-222-2-2-2-12-2-2-22-22-1-1-1-1-1-1-111-1-1111-111-11−2i2i−2i2i00000000ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i333−3−333−3−30000000000000000
χ3122222-2-2-22-2222-22-2-22-22222222-2-2-2-222-2-22-2-222i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ3222222-2-2-22-2222-22-2-22-22222222-2-2-2-222-2-22-2-22−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ3322222-2-2-22-22-12-22-2-22-2-1-1-1-1-1-1-11111-1-111-111-12i−2i−2i2i00000000−i−iiiii−i−i33−3−3−3−333i3i3−i3−i3−i3−i3i3i30000000000000000
χ3422222-2-2-22-22-12-22-2-22-2-1-1-1-1-1-1-11111-1-111-111-12i−2i−2i2i00000000−i−iiiii−i−i−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3522222-2-2-22-22-12-22-2-22-2-1-1-1-1-1-1-11111-1-111-111-1−2i2i2i−2i00000000ii−i−i−i−iii33−3−3−3−333−i3−i3i3i3i3i3−i3−i30000000000000000
χ3622222-2-2-22-22-12-22-2-22-2-1-1-1-1-1-1-11111-1-111-111-1−2i2i2i−2i00000000ii−i−i−i−iii−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000000000000000
χ372222-222-22-2-22-2-222-2-22-2-2222-2-22-22-22-2-2222-2-200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ382222-222-22-2-22-2-222-2-22-2-2222-2-22-22-22-2-2222-2-20000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ392222-222-22-2-2-1-2-222-2-2211-1-1-111-11-11-111-1-1-11100002i−2i2i−2i0000−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii3−33−33−33−30000000000000000
χ402222-222-22-2-2-1-2-222-2-2211-1-1-111-11-11-111-1-1-11100002i−2i2i−2i0000i3−i3i3−i3i3−i3i3−i3−ii−ii−ii−ii−33−33−33−330000000000000000
χ412222-222-22-2-2-1-2-222-2-2211-1-1-111-11-11-111-1-1-1110000−2i2i−2i2i0000−i3i3−i3i3−i3i3−i3i3i−ii−ii−ii−i−33−33−33−330000000000000000
χ422222-222-22-2-2-1-2-222-2-2211-1-1-111-11-11-111-1-1-1110000−2i2i−2i2i0000i3−i3i3−i3i3−i3i3−i3i−ii−ii−ii−i3−33−33−33−30000000000000000
χ432222-22-22-2-222-2-2-2222-2-2-2222-2-22-2-22-22-2-2-222200002-2-220000000000002-22-2-22-22000000000000000000000000
χ442222-22-22-2-222-2-2-2222-2-2-2222-2-22-2-22-22-2-2-22220000-222-2000000000000-22-222-22-2000000000000000000000000
χ452222-22-22-2-22-1-2-2-2222-211-1-1-111-111-11-1111-1-1-100002-2-220000−i3i3−i3i3i3−i3i3−i3-11-111-11-1−i3i3−i3i3i3−i3i3−i30000000000000000
χ462222-22-22-2-22-1-2-2-2222-211-1-1-111-111-11-1111-1-1-100002-2-220000i3−i3i3−i3−i3i3−i3i3-11-111-11-1i3−i3i3−i3−i3i3−i3i30000000000000000
χ472222-22-22-2-22-1-2-2-2222-211-1-1-111-111-11-1111-1-1-10000-222-20000−i3i3−i3i3i3−i3i3−i31-11-1-11-11i3−i3i3−i3−i3i3−i3i30000000000000000
χ482222-22-22-2-22-1-2-2-2222-211-1-1-111-111-11-1111-1-1-10000-222-20000i3−i3i3−i3−i3i3−i3i31-11-1-11-11−i3i3−i3i3i3−i3i3−i30000000000000000
χ492222-2-22-2-2222-22-2-2-222-2-2222-2-2-222-2-2222-2-2-22000000002-22-200000000000000002-2-222-2-220000000000000000
χ502222-2-22-2-2222-22-2-2-222-2-2222-2-2-222-2-2222-2-2-2200000000-22-220000000000000000-222-2-222-20000000000000000
χ512222-2-22-2-222-1-22-2-2-22211-1-1-1111-1-111-1-1-1111-1000000002-22-23−3−333−3−33−333−3−333−3-111-1-111-10000000000000000
χ522222-2-22-2-222-1-22-2-2-22211-1-1-1111-1-111-1-1-1111-1000000002-22-2−333−3−333−33−3−333−3−33-111-1-111-10000000000000000
χ532222-2-22-2-222-1-22-2-2-22211-1-1-1111-1-111-1-1-1111-100000000-22-223−3−333−3−333−3−333−3−331-1-111-1-110000000000000000
χ542222-2-22-2-222-1-22-2-2-22211-1-1-1111-1-111-1-1-1111-100000000-22-22−333−3−333−3−333−3−333−31-1-111-1-110000000000000000
χ552222-2-2-2222-22-222-22-2-2-2-2222-2-2-22-222-22-22-22-2000000002i−2i−2i2i00000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ562222-2-2-2222-22-222-22-2-2-2-2222-2-2-22-222-22-22-22-200000000−2i2i2i−2i0000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ572222-2-2-2222-2-1-222-22-2-211-1-1-1111-11-1-11-11-11-11000000002i−2i−2i2i3−3−33−333−3−i3i3i3−i3i3−i3−i3i3−iii−ii−i−ii0000000000000000
χ582222-2-2-2222-2-1-222-22-2-211-1-1-1111-11-1-11-11-11-11000000002i−2i−2i2i−333−33−3−33i3−i3−i3i3−i3i3i3−i3−iii−ii−i−ii0000000000000000
χ592222-2-2-2222-2-1-222-22-2-211-1-1-1111-11-1-11-11-11-1100000000−2i2i2i−2i3−3−33−333−3i3−i3−i3i3−i3i3i3−i3i−i−ii−iii−i0000000000000000
χ602222-2-2-2222-2-1-222-22-2-211-1-1-1111-11-1-11-11-11-1100000000−2i2i2i−2i−333−33−3−33−i3i3i3−i3i3−i3−i3i3i−i−ii−iii−i0000000000000000
χ6122-2-222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ6222-2-222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ6322-2-222-2-2-22-22-2-22-2222222-2-2-2-222-2-2-2-2-222-2220000000000000000000000000000000000000000000000002-2-22
χ6422-2-222-2-2-22-22-2-22-2222222-2-2-2-222-2-2-2-2-222-222000000000000000000000000000000000000000000000000-222-2
χ6522-2-22-222-2-2-22-2222-22-2222-2-2-2-2-2-222-2-22-222-22000000000000000000000000000000000000000000002i−2i2i−2i0000
χ6622-2-22-222-2-2-22-2222-22-2222-2-2-2-2-2-222-2-22-222-2200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ6722-2-22-2-2-22-222-22-222-22222-2-2-2-2-2-2-2-22222-222-2000000000000000000000000000000000000000000002-2-220000
χ6822-2-22-2-2-22-222-22-222-22222-2-2-2-2-2-2-2-22222-222-200000000000000000000000000000000000000000000-222-20000
χ6922-2-2-222-22-2-2222-2-222-2-2-22-2-2222-22-22-22-2-2-22200000000000000000000000000000000000000002i−2i2i−2i00000000
χ7022-2-2-222-22-2-2222-2-222-2-2-22-2-2222-22-22-22-2-2-2220000000000000000000000000000000000000000−2i2i−2i2i00000000
χ7122-2-2-22-22-2-222222-2-2-22-2-22-2-2222-2-22-22222-2-2-200000000000000000000000000000000000000002i−2i−2i2i00000000
χ7222-2-2-22-22-2-222222-2-2-22-2-22-2-2222-2-22-22222-2-2-20000000000000000000000000000000000000000−2i2i2i−2i00000000
χ7322-2-2-2-22-2-22222-2222-2-2-2-22-2-222-222-2-22-2-2222-20000000000000000000000000000000000002-2-22000000000000
χ7422-2-2-2-22-2-22222-2222-2-2-2-22-2-222-222-2-22-2-2222-2000000000000000000000000000000000000-222-2000000000000
χ7522-2-2-2-2-2222-222-2-22-222-2-22-2-222-22-222-2-22-22-2200000000000000000000000000000000000022-2-2000000000000
χ7622-2-2-2-2-2222-222-2-22-222-2-22-2-222-22-222-2-22-22-22000000000000000000000000000000000000-2-222000000000000
χ7744-4-44444444-2-4-4-4-4-4-4-4-2-2-22222-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000000
χ7844-4-444-4-4-44-4-2-4-44-4444-2-2-22222-2-222222-2-22-2-20000000000000000000000000000000000000000000000000000
χ7944-4-44-444-4-4-4-2-4444-44-4-2-2-2222222-2-222-22-2-22-20000000000000000000000000000000000000000000000000000
χ8044-4-44-4-4-44-44-2-44-444-44-2-2-222222222-2-2-2-22-2-220000000000000000000000000000000000000000000000000000
χ8144-4-4-444-44-4-4-244-4-444-422-222-2-2-22-22-22-2222-2-20000000000000000000000000000000000000000000000000000
χ8244-4-4-44-44-4-44-2444-4-4-4422-222-2-2-222-22-2-2-2-22220000000000000000000000000000000000000000000000000000
χ8344-4-4-4-44-4-444-24-4444-4-422-222-2-22-2-222-222-2-2-220000000000000000000000000000000000000000000000000000
χ8444-4-4-4-4-4444-4-24-4-44-44422-222-2-22-22-2-222-22-22-20000000000000000000000000000000000000000000000000000
χ858-88i−8i00000008000000000-88i−8i000000000000000000000000000000000000000000000000000000000000000000
χ868-88i−8i0000000-40000000−4i34i34−4i4i43−430000000000000000000000000000000000000000000000000000000000000000
χ878-88i−8i0000000-400000004i3−4i34−4i4i−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8−8i8i00000008000000000-8−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ898-8−8i8i0000000-40000000−4i34i344i−4i−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8−8i8i0000000-400000004i3−4i344i−4i43−430000000000000000000000000000000000000000000000000000000000000000

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