Finite Group Databasebeta

← Group #10702936

Character table — Group #10702936

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order124422222223444444466612121212666666121212121212224444446666888812121212121212121212121224242424242424244444444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911-1-111-11-1-1-11111-1-11-1111-1-1-1-111-1-1-1-1111-1-1111-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-111-11-1-1-11111-1-11-1111-1-1-1-111-1-1-1-1111-1-1111-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-111-11-1-1-11111-1-11-1111-1-1-1-111-1-1-1-1111-1-1111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-111-11-1-1-11111-1-11-1111-1-1-1-111-1-1-1-1111-1-1111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-111-11-1-1-11111-1-11-1111-1-1-1-111-1-1-1-1111-1-11-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411-1-111-11-1-1-11111-1-11-1111-1-1-1-111-1-1-1-1111-1-11-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511-1-111-11-1-1-11111-1-11-1111-1-1-1-111-1-1-1-1111-1-11-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611-1-111-11-1-1-11111-1-11-1111-1-1-1-111-1-1-1-1111-1-11-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-2-2-2-211111111-1-1-1-1111111110000000000000000
χ1922222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111-2-2-2-2-1-1-1-1-1-1-1-11111111111110000000000000000
χ2022222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211112222111111111111-1-1-1-1-1-1-1-10000000000000000
χ21222222-22-2-2-22-2-2-222-22222222222-2-2-2-2-2-2-222-20000000000000000000000000000000000002i−2i2i−2i000000000000
χ22222222-22-2-2-22-2-2-222-22222222222-2-2-2-2-2-2-222-2000000000000000000000000000000000000−2i2i−2i2i000000000000
χ2322222-22-22-2-2222-2-2-2-22-2-2222-2-22-222-2-222-22-2-200002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ2422222-22-22-2-2222-2-2-2-22-2-2222-2-22-222-2-222-22-2-20000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ2522222-22-22-2-2-122-2-2-2-2211-1-1-111-11-1-111-1-11-11100002i−2i2i−2i−i3−i3i3i30000−i−iii−i−iii−i3−i3i3i333−3−333−3−30000000000000000
χ2622222-22-22-2-2-122-2-2-2-2211-1-1-111-11-1-111-1-11-11100002i−2i2i−2ii3i3−i3−i30000−i−iii−i−iiii3i3−i3−i3−3−333−3−3330000000000000000
χ2722222-22-22-2-2-122-2-2-2-2211-1-1-111-11-1-111-1-11-1110000−2i2i−2i2i−i3−i3i3i30000ii−i−iii−i−i−i3−i3i3i3−3−333−3−3330000000000000000
χ2822222-22-22-2-2-122-2-2-2-2211-1-1-111-11-1-111-1-11-1110000−2i2i−2i2ii3i3−i3−i30000ii−i−iii−i−ii3i3−i3−i333−3−333−3−30000000000000000
χ2922222-2-2-2-2222-2-22-2-222-2-2222-2-22-2-2-222-2-222-22000000000000000000000000000000000000000000002-22-20000
χ3022222-2-2-2-2222-2-22-2-222-2-2222-2-22-2-2-222-2-222-2200000000000000000000000000000000000000000000-22-220000
χ312222-222-2-22-222-2-22-22-2-2-2222-2-2-222-22-22-2-2-2220000000000000000000000000000000000000000000000002i−2i2i−2i
χ322222-222-2-22-222-2-22-22-2-2-2222-2-2-222-22-22-2-2-222000000000000000000000000000000000000000000000000−2i2i−2i2i
χ332222-22-2-22-222-2222-2-2-2-2-2222-2-2-22-22-22-222-22-20000000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ342222-22-2-22-222-2222-2-2-2-2-2222-2-2-22-22-22-222-22-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ352222-22-2-22-22-1-2222-2-2-211-1-1-1111-11-11-11-1-11-1100000000−i3i3−i3i32i−2i2i−2i3−33−33−33−3−i3i3−i3i3−ii−ii−ii−ii0000000000000000
χ362222-22-2-22-22-1-2222-2-2-211-1-1-1111-11-11-11-1-11-1100000000−i3i3−i3i3−2i2i−2i2i−33−33−33−33−i3i3−i3i3i−ii−ii−ii−i0000000000000000
χ372222-22-2-22-22-1-2222-2-2-211-1-1-1111-11-11-11-1-11-1100000000i3−i3i3−i32i−2i2i−2i−33−33−33−33i3−i3i3−i3−ii−ii−ii−ii0000000000000000
χ382222-22-2-22-22-1-2222-2-2-211-1-1-1111-11-11-11-1-11-1100000000i3−i3i3−i3−2i2i−2i2i3−33−33−33−3i3−i3i3−i3i−ii−ii−ii−i0000000000000000
χ392222-2-222-2-2222-22-22-2-22222222-2-22-2-222-22-2-2-200000000000000000000000000000000000000002i−2i2i−2i00000000
χ402222-2-222-2-2222-22-22-2-22222222-2-22-2-222-22-2-2-20000000000000000000000000000000000000000−2i2i−2i2i00000000
χ412222-2-2-2222-22-22-2-222-22222222-2-2-222-2-22-2-2-222-22-200002-2-220000000000002-2-22000000000000000000000000
χ422222-2-2-2222-22-22-2-222-22222222-2-2-222-2-22-2-2-22-22-220000-222-2000000000000-222-2000000000000000000000000
χ432222-2-2-2222-2-1-22-2-222-2-1-1-1-1-1-1-1111-1-111-1111-12-22-20000-111-10000−i3i3i3−i3−i3i3i3−i3-111-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ442222-2-2-2222-2-1-22-2-222-2-1-1-1-1-1-1-1111-1-111-1111-12-22-20000-111-10000i3−i3−i3i3i3−i3−i3i3-111-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ452222-2-2-2222-2-1-22-2-222-2-1-1-1-1-1-1-1111-1-111-1111-1-22-2200001-1-110000−i3i3i3−i3−i3i3i3−i31-1-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ462222-2-2-2222-2-1-22-2-222-2-1-1-1-1-1-1-1111-1-111-1111-1-22-2200001-1-110000i3−i3−i3i3i3−i3−i3i31-1-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ4722-2-222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000002-2-22000000000000
χ4822-2-222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000-222-2000000000000
χ4922-2-222-22-2-2-2-1222-2-22-2-1-1-11111-1-11111-1-1-111-122-2-222-2-2-1-1-1-122-2-2-1-1-1-111111111-1-1-1-111110000000000000000
χ5022-2-222-22-2-2-2-1222-2-22-2-1-1-11111-1-11111-1-1-111-122-2-2-2-222-1-1-1-1-2-2221111-1-1-1-111111111-1-1-1-10000000000000000
χ5122-2-222-22-2-2-2-1222-2-22-2-1-1-11111-1-11111-1-1-111-1-2-22222-2-21111-2-222-1-1-1-11111-1-1-1-11111-1-1-1-10000000000000000
χ5222-2-222-22-2-2-2-1222-2-22-2-1-1-11111-1-11111-1-1-111-1-2-222-2-222111122-2-21111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ5322-2-22-22-22-2-22-2-22222-2-2-22-2-2222-222-2-2-2-22-222000000000000000000000000000000000000000000002i−2i−2i2i0000
χ5422-2-22-22-22-2-22-2-22222-2-2-22-2-2222-222-2-2-2-22-22200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ5522-2-22-2-2-2-222222-222-2-2-2-22-2-2222-2-2-22222-2-22-200002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ5622-2-22-2-2-2-222222-222-2-2-2-22-2-2222-2-2-22222-2-22-20000−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ5722-2-22-2-2-2-222-122-222-2-211-111-1-1-1111-1-1-1-111-1100002i−2i−2i2i−i3−i3i3i30000−i−iiiii−i−ii3i3−i3−i333−3−3−3−3330000000000000000
χ5822-2-22-2-2-2-222-122-222-2-211-111-1-1-1111-1-1-1-111-1100002i−2i−2i2ii3i3−i3−i30000−i−iiiii−i−i−i3−i3i3i3−3−33333−3−30000000000000000
χ5922-2-22-2-2-2-222-122-222-2-211-111-1-1-1111-1-1-1-111-110000−2i2i2i−2i−i3−i3i3i30000ii−i−i−i−iiii3i3−i3−i3−3−33333−3−30000000000000000
χ6022-2-22-2-2-2-222-122-222-2-211-111-1-1-1111-1-1-1-111-110000−2i2i2i−2ii3i3−i3−i30000ii−i−i−i−iii−i3−i3i3i333−3−3−3−3330000000000000000
χ6122-2-2-222-2-22-22-222-22-22-2-22-2-222-222-22-2-2222-2-20000000000002i−2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ6222-2-2-222-2-22-22-222-22-22-2-22-2-222-222-22-2-2222-2-2000000000000−2i2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ6322-2-2-222-2-22-2-1-222-22-2211-111-1-11-1-11-111-1-1-11100000000−i3i3−i3i32i−2i−2i2i3−33−3−33−33i3−i3i3−i3−ii−iii−ii−i0000000000000000
χ6422-2-2-222-2-22-2-1-222-22-2211-111-1-11-1-11-111-1-1-11100000000−i3i3−i3i3−2i2i2i−2i−33−333−33−3i3−i3i3−i3i−ii−i−ii−ii0000000000000000
χ6522-2-2-222-2-22-2-1-222-22-2211-111-1-11-1-11-111-1-1-11100000000i3−i3i3−i32i−2i−2i2i−33−333−33−3−i3i3−i3i3−ii−iii−ii−i0000000000000000
χ6622-2-2-222-2-22-2-1-222-22-2211-111-1-11-1-11-111-1-1-11100000000i3−i3i3−i3−2i2i2i−2i3−33−3−33−33−i3i3−i3i3i−ii−i−ii−ii0000000000000000
χ6722-2-2-22-2-22-2222-2-2-2222-2-22-2-222-22-22-222-2-22-220000000000000000000000000000000000000000000000002-2-22
χ6822-2-2-22-2-22-2222-2-2-2222-2-22-2-222-22-22-222-2-22-22000000000000000000000000000000000000000000000000-222-2
χ6922-2-2-2-222-2-222-22-22-222222-2-2-2-2-2-22-2-22-22-22222-2-2200002-2-22000000000000-222-2000000000000000000000000
χ7022-2-2-2-222-2-222-22-22-222222-2-2-2-2-2-22-2-22-22-2222-222-20000-222-20000000000002-2-22000000000000000000000000
χ7122-2-2-2-222-2-22-1-22-22-222-1-1-1111111-111-11-11-1-1-12-2-220000-111-10000−i3i3i3−i3i3−i3−i3i31-1-11−i3i3i3−i3i3−i3−i3i30000000000000000
χ7222-2-2-2-222-2-22-1-22-22-222-1-1-1111111-111-11-11-1-1-12-2-220000-111-10000i3−i3−i3i3−i3i3i3−i31-1-11i3−i3−i3i3−i3i3i3−i30000000000000000
χ7322-2-2-2-222-2-22-1-22-22-222-1-1-1111111-111-11-11-1-1-1-222-200001-1-110000−i3i3i3−i3i3−i3−i3i3-111-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ7422-2-2-2-222-2-22-1-22-22-222-1-1-1111111-111-11-11-1-1-1-222-200001-1-110000i3−i3−i3i3−i3i3i3−i3-111-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ7522-2-2-2-2-2222-222-222-2-22222-2-2-2-2-2-2-222-22-2222-200000000000000000000000000000000000000002-2-2200000000
χ7622-2-2-2-2-2222-222-222-2-22222-2-2-2-2-2-2-222-22-2222-20000000000000000000000000000000000000000-222-200000000
χ77444444-44-4-4-4-2-4-4-444-44-2-2-2-2-2-2-2-2-22222222-2-220000000000000000000000000000000000000000000000000000
χ7844444-4-4-4-444-2-4-44-4-44422-2-2-222-2222-2-222-2-22-20000000000000000000000000000000000000000000000000000
χ794444-444-4-44-4-24-4-44-44-422-2-2-2222-2-22-22-2222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-444-4-44-24-44-44-4-4-2-2-2-2-2-2-222-222-2-22-22220000000000000000000000000000000000000000000000000000
χ8144-4-44444444-2-4-4-4-4-4-4-4-2-2-22222-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000000
χ8244-4-44-44-44-4-4-2-4-44444-422-222-2-2-22-2-22222-22-2-20000000000000000000000000000000000000000000000000000
χ8344-4-4-44-4-44-44-24-4-4-444422-222-2-22-22-22-2-222-22-20000000000000000000000000000000000000000000000000000
χ8444-4-4-4-4-4444-4-24-444-4-44-2-2-22222222-2-22-22-2-2-220000000000000000000000000000000000000000000000000000
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).