Finite Group Databasebeta

← Group #10702931

Character table — Group #10702931

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1244222222234444444666121212126666661212121212124444888888881212121212121212242424242424242424242424242424242244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ9111111-1-1-1-11111-11-1-1-1111111111-1-1-1-111-1-1-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-111-1-1ii−i−iii−i−i
χ10111111-1-1-1-11111-11-1-1-1111111111-1-1-1-111-1-1-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-11-1-111−i−iii−i−iii
χ11111111-1-1-1-11111-11-1-1-1111111111-1-1-1-111-1-1-1-1ii−i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-11-1-1-111ii−i−i−i−iii
χ12111111-1-1-1-11111-11-1-1-1111111111-1-1-1-111-1-1-1-1ii−i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-1111-1-1−i−iiiii−i−i
χ13111111-1-1-1-11111-11-1-1-1111111111-1-1-1-111-1-1-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-11-111-1-1−i−iii−i−iii
χ14111111-1-1-1-11111-11-1-1-1111111111-1-1-1-111-1-1-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-11-1-111ii−i−iii−i−i
χ15111111-1-1-1-11111-11-1-1-1111111111-1-1-1-111-1-1-1-1−i−iii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-11-1-1-111−i−iiiii−i−i
χ16111111-1-1-1-11111-11-1-1-1111111111-1-1-1-111-1-1-1-1−i−iii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−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
χ21222222-2-2-2-22-122-22-2-2-2-1-1-1-1-1-1-1-1-11111-1-111112i2i−2i−2i22-2-22i2i−2i−2i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii0000000000000000
χ22222222-2-2-2-22-122-22-2-2-2-1-1-1-1-1-1-1-1-11111-1-111112i2i−2i−2i-2-222−2i−2i2i2i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i0000000000000000
χ23222222-2-2-2-22-122-22-2-2-2-1-1-1-1-1-1-1-1-11111-1-11111−2i−2i2i2i22-2-2−2i−2i2i2iiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ24222222-2-2-2-22-122-22-2-2-2-1-1-1-1-1-1-1-1-11111-1-11111−2i−2i2i2i-2-2222i2i−2i−2iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii0000000000000000
χ2522222-222-2-2-222-2-2-222-2-2-2222-2-22-222-2-22-22-2-2200002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2622222-222-2-2-222-2-2-222-2-2-2222-2-22-222-2-22-22-2-220000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2722222-222-2-2-2-12-2-2-222-211-1-1-111-11-1-111-11-111-100002i−2i2i−2i000033−3−333−3−3−i−iii−i−iii−i3−i3i3i3−i3−i3i3i30000000000000000
χ2822222-222-2-2-2-12-2-2-222-211-1-1-111-11-1-111-11-111-100002i−2i2i−2i0000−3−333−3−333−i−iii−i−iiii3i3−i3−i3i3i3−i3−i30000000000000000
χ2922222-222-2-2-2-12-2-2-222-211-1-1-111-11-1-111-11-111-10000−2i2i−2i2i000033−3−333−3−3ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i30000000000000000
χ3022222-222-2-2-2-12-2-2-222-211-1-1-111-11-1-111-11-111-10000−2i2i−2i2i0000−3−333−3−333ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i30000000000000000
χ3122222-2-2-222-222-22-2-2-22-2-2222-2-22-2-2-2222-2-222-200002i−2i−2i2i0000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ3222222-2-2-222-222-22-2-2-22-2-2222-2-22-2-2-2222-2-222-20000−2i2i2i−2i000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ3322222-2-2-222-2-12-22-2-2-2211-1-1-111-1111-1-1-111-1-1100002i−2i−2i2i0000−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i−3−33333−3−30000000000000000
χ3422222-2-2-222-2-12-22-2-2-2211-1-1-111-1111-1-1-111-1-1100002i−2i−2i2i0000i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i33−3−3−3−3330000000000000000
χ3522222-2-2-222-2-12-22-2-2-2211-1-1-111-1111-1-1-111-1-110000−2i2i2i−2i0000−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii33−3−3−3−3330000000000000000
χ3622222-2-2-222-2-12-22-2-2-2211-1-1-111-1111-1-1-111-1-110000−2i2i2i−2i0000i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii−3−33333−3−30000000000000000
χ372222-222-22-2-22-2-2222-2-22222222-2-22-22-2-2-2-22-22000000000000000000000000000000000000000000002i−2i2i−2i0000
χ382222-222-22-2-22-2-2222-2-22222222-2-22-22-2-2-2-22-2200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ392222-22-22-22-22-2-2-22-2222222222-2-2-22-22-2-22-22-2000000000000000000000000000000000000000000002-2-220000
χ402222-22-22-22-22-2-2-22-2222222222-2-2-22-22-2-22-22-200000000000000000000000000000000000000000000-222-20000
χ412222-2-22-2-2222-22-2-22-22-2-2222-2-2-222-2-22-22-2-2220000000000000000000000000000000000000000000000002-22-2
χ422222-2-22-2-2222-22-2-22-22-2-2222-2-2-222-2-22-22-2-222000000000000000000000000000000000000000000000000-22-22
χ432222-2-2-222-222-222-2-22-2-2-2222-2-2-22-222-2-2222-2-20000000000000000000000000000000000000000000000002i−2i−2i2i
χ442222-2-2-222-222-222-2-22-2-2-2222-2-2-22-222-2-2222-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i
χ4522-2-222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ4622-2-222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ4722-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111000000002i−2i2i−2i−i3i3−i3i3−i3i3−i3i33−33−33−33−3−ii−ii−ii−ii0000000000000000
χ4822-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111000000002i−2i2i−2ii3−i3i3−i3i3−i3i3−i3−33−33−33−33−ii−ii−ii−ii0000000000000000
χ4922-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100000000−2i2i−2i2i−i3i3−i3i3−i3i3−i3i3−33−33−33−33i−ii−ii−ii−i0000000000000000
χ5022-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100000000−2i2i−2i2ii3−i3i3−i3i3−i3i3−i33−33−33−33−3i−ii−ii−ii−i0000000000000000
χ5122-2-222-2-2-2-222-2-22-2222222-2-2-2-222-2-2-2-2-2-22222000000002-2-2200000000000000002-22-2-22-220000000000000000
χ5222-2-222-2-2-2-222-2-22-2222222-2-2-2-222-2-2-2-2-2-2222200000000-222-20000000000000000-22-222-22-20000000000000000
χ5322-2-222-2-2-2-22-1-2-22-2222-1-1-11111-1-1111111-1-1-1-1000000002-2-223−33−3−33−33−33−333−33−3-11-111-11-10000000000000000
χ5422-2-222-2-2-2-22-1-2-22-2222-1-1-11111-1-1111111-1-1-1-1000000002-2-22−33−333−33−33−33−3−33−33-11-111-11-10000000000000000
χ5522-2-222-2-2-2-22-1-2-22-2222-1-1-11111-1-1111111-1-1-1-100000000-222-23−33−3−33−333−33−3−33−331-11-1-11-110000000000000000
χ5622-2-222-2-2-2-22-1-2-22-2222-1-1-11111-1-1111111-1-1-1-100000000-222-2−33−333−33−3−33−333−33−31-11-1-11-110000000000000000
χ5722-2-22-222-2-2-22-2222-2-22-2-22-2-2222-222-2-2-22-222-22i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ5822-2-22-222-2-2-22-2222-2-22-2-22-2-2222-222-2-2-22-222-2−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ5922-2-22-222-2-2-2-1-2222-2-2211-111-1-1-11-1-1111-11-1-112i−2i2i−2i00000000−iii−i−iii−i−i3i3i3−i3−i3i3i3−i3−333−3−333−30000000000000000
χ6022-2-22-222-2-2-2-1-2222-2-2211-111-1-1-11-1-1111-11-1-112i−2i2i−2i00000000−iii−i−iii−ii3−i3−i3i3i3−i3−i3i33−3−333−3−330000000000000000
χ6122-2-22-222-2-2-2-1-2222-2-2211-111-1-1-11-1-1111-11-1-11−2i2i−2i2i00000000i−i−iii−i−ii−i3i3i3−i3−i3i3i3−i33−3−333−3−330000000000000000
χ6222-2-22-222-2-2-2-1-2222-2-2211-111-1-1-11-1-1111-11-1-11−2i2i−2i2i00000000i−i−iii−i−iii3−i3−i3i3i3−i3−i3i3−333−3−333−30000000000000000
χ6322-2-22-2-2-222-22-22-2222-2-2-22-2-2222-2-2-222-222-2-222-2-22000000002-2-22-222-200000000000000000000000000000000
χ6422-2-22-2-2-222-22-22-2222-2-2-22-2-2222-2-2-222-222-2-22-222-200000000-222-22-2-2200000000000000000000000000000000
χ6522-2-22-2-2-222-2-1-22-2222-211-111-1-1-1111-1-11-1-111-12-2-2200000000-111-11-1-11−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ6622-2-22-2-2-222-2-1-22-2222-211-111-1-1-1111-1-11-1-111-12-2-2200000000-111-11-1-11i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ6722-2-22-2-2-222-2-1-22-2222-211-111-1-1-1111-1-11-1-111-1-222-2000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ6822-2-22-2-2-222-2-1-22-2222-211-111-1-1-1111-1-11-1-111-1-222-2000000001-1-11-111-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ6922-2-2-222-22-2-2222-2-2-222222-2-2-2-2-2-22-22-2222-22-200000000000000000000000000000000000000002i−2i2i−2i00000000
χ7022-2-2-222-22-2-2222-2-2-222222-2-2-2-2-2-22-22-2222-22-20000000000000000000000000000000000000000−2i2i−2i2i00000000
χ7122-2-2-22-22-22-22222-22-2-2222-2-2-2-2-2-2-22-2222-22-2200000000000000000000000000000000000000002i−2i−2i2i00000000
χ7222-2-2-22-22-22-22222-22-2-2222-2-2-2-2-2-2-22-2222-22-220000000000000000000000000000000000000000−2i2i2i−2i00000000
χ7322-2-2-2-22-2-22222-222-22-2-2-22-2-222-222-2-222-222-2-20000000000000000000000000000000000002-2-22000000000000
χ7422-2-2-2-22-2-22222-222-22-2-2-22-2-222-222-2-222-222-2-2000000000000000000000000000000000000-222-2000000000000
χ7522-2-2-2-2-222-2222-2-222-22-2-22-2-222-22-222-22-2-2-22200000000000000000000000000000000000022-2-2000000000000
χ7622-2-2-2-2-222-2222-2-222-22-2-22-2-222-22-222-22-2-2-222000000000000000000000000000000000000-2-222000000000000
χ774444-444-44-4-4-2-4-4444-4-4-2-2-2-2-2-2-222-22-22222-22-20000000000000000000000000000000000000000000000000000
χ784444-44-44-44-4-2-4-4-44-444-2-2-2-2-2-2-2222-22-222-22-220000000000000000000000000000000000000000000000000000
χ794444-4-44-4-444-2-44-4-44-4422-2-2-2222-2-222-22-222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-4-444-44-2-444-4-44-422-2-2-2222-22-2-222-2-2-2220000000000000000000000000000000000000000000000000000
χ8144-4-4-444-44-4-4-244-4-4-444-2-2-2222222-22-22-2-2-22-220000000000000000000000000000000000000000000000000000
χ8244-4-4-44-44-44-4-2444-44-4-4-2-2-22222222-22-2-2-22-22-20000000000000000000000000000000000000000000000000000
χ8344-4-4-4-44-4-444-24-444-44-422-222-2-22-2-222-2-22-2-2220000000000000000000000000000000000000000000000000000
χ8444-4-4-4-4-444-44-24-4-444-4422-222-2-22-22-2-22-2222-2-20000000000000000000000000000000000000000000000000000
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).