Finite Group Databasebeta

← Group #10702894

Character table — Group #10702894

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order122222222234444444466612121212666666121212121212224466668888888812121212242424242424242424242424242424244444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ911111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-11-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-11-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-11-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-11-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-11-11-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-11-11-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-11-11-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-11-11-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111110000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111110000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-22-2-1-1112i2i−2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ222222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-22-2-1-111−2i−2i2i2i−2i−2i2i2i-1-111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-22-2211-1-12i2i−2i−2i−2i−2i2i2i11-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-22-2211-1-1−2i−2i2i2i2i2i−2i−2i11-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ25222222-2-2-2-22222-2-2-22-2222-2-2-2-222-2-2-2-22222-2-20000000000002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ26222222-2-2-2-22222-2-2-22-2222-2-2-2-222-2-2-2-22222-2-2000000000000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ27222222-2-2-2-22-2-2-2222-22222222222-2-2-2-2-2-2-2-2220000000000002-2-2200000000000022-2-2-2-2220000000000000000
χ28222222-2-2-2-22-2-2-2222-22222222222-2-2-2-2-2-2-2-222000000000000-222-2000000000000-2-22222-2-20000000000000000
χ29222222-2-2-2-2-1222-2-2-22-2-1-1-11111-1-11111-1-1-1-1110000−i3i3−i3i300002i−2i2i−2i−i3i3−i3i333−3−333−3−3−i−iii−i−iii0000000000000000
χ30222222-2-2-2-2-1222-2-2-22-2-1-1-11111-1-11111-1-1-1-1110000−i3i3−i3i30000−2i2i−2i2i−i3i3−i3i3−3−333−3−333ii−i−iii−i−i0000000000000000
χ31222222-2-2-2-2-1222-2-2-22-2-1-1-11111-1-11111-1-1-1-1110000i3−i3i3−i300002i−2i2i−2ii3−i3i3−i3−3−333−3−333−i−iii−i−iii0000000000000000
χ32222222-2-2-2-2-1222-2-2-22-2-1-1-11111-1-11111-1-1-1-1110000i3−i3i3−i30000−2i2i−2i2ii3−i3i3−i333−3−333−3−3ii−i−iii−i−i0000000000000000
χ33222222-2-2-2-2-1-2-2-2222-22-1-1-1-1-1-1-1-1-111111111-1-10000−i3i3i3−i300002-2-22−i3i3i3−i3−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000000000
χ34222222-2-2-2-2-1-2-2-2222-22-1-1-1-1-1-1-1-1-111111111-1-10000−i3i3i3−i30000-222-2−i3i3i3−i3i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000000000
χ35222222-2-2-2-2-1-2-2-2222-22-1-1-1-1-1-1-1-1-111111111-1-10000i3−i3−i3i300002-2-22i3−i3−i3i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000000000
χ36222222-2-2-2-2-1-2-2-2222-22-1-1-1-1-1-1-1-1-111111111-1-10000i3−i3−i3i30000-222-2i3−i3−i3i3−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000000000
χ372222-2-222-2-2222-22-2-2-22222-2-2-2-2-2-222-2-222-2-222000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ382222-2-222-2-2222-22-2-2-22222-2-2-2-2-2-222-2-222-2-22200000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ392222-2-222-2-22-2-22-2222-22222222-2-222-2-2-2-222-2-2000000002-2-22000000002-22-2-22-22000000000000000000000000
χ402222-2-222-2-22-2-22-2222-22222222-2-222-2-2-2-222-2-200000000-222-200000000-22-222-22-2000000000000000000000000
χ412222-2-222-2-2-122-22-2-2-22-1-1-1111111-1-111-1-111-1-10000−i3i3i3−i32i−2i2i−2i0000i3−i3−i3i3−ii−ii−ii−ii3−33−33−33−30000000000000000
χ422222-2-222-2-2-122-22-2-2-22-1-1-1111111-1-111-1-111-1-10000−i3i3i3−i3−2i2i−2i2i0000i3−i3−i3i3i−ii−ii−ii−i−33−33−33−330000000000000000
χ432222-2-222-2-2-122-22-2-2-22-1-1-1111111-1-111-1-111-1-10000i3−i3−i3i32i−2i2i−2i0000−i3i3i3−i3−ii−ii−ii−ii−33−33−33−330000000000000000
χ442222-2-222-2-2-122-22-2-2-22-1-1-1111111-1-111-1-111-1-10000i3−i3−i3i3−2i2i−2i2i0000−i3i3i3−i3i−ii−ii−ii−i3−33−33−33−30000000000000000
χ452222-2-222-2-2-1-2-22-2222-2-1-1-1-1-1-1-111-1-11111-1-1110000−i3i3−i3i32-2-220000i3−i3i3−i3-11-111-11-1−i3i3−i3i3i3−i3i3−i30000000000000000
χ462222-2-222-2-2-1-2-22-2222-2-1-1-1-1-1-1-111-1-11111-1-1110000−i3i3−i3i3-222-20000i3−i3i3−i31-11-1-11-11i3−i3i3−i3−i3i3−i3i30000000000000000
χ472222-2-222-2-2-1-2-22-2222-2-1-1-1-1-1-1-111-1-11111-1-1110000i3−i3i3−i32-2-220000−i3i3−i3i3-11-111-11-1i3−i3i3−i3−i3i3−i3i30000000000000000
χ482222-2-222-2-2-1-2-22-2222-2-1-1-1-1-1-1-111-1-11111-1-1110000i3−i3i3−i3-222-20000−i3i3−i3i31-11-1-11-11−i3i3−i3i3i3−i3i3−i30000000000000000
χ492222-2-2-2-222222-2-222-2-22222222-2-2-2-22222-2-2-2-22-2-2222-2-200000000-2-22200000000000000000000000000000000
χ502222-2-2-2-222222-2-222-2-22222222-2-2-2-22222-2-2-2-2-222-2-2-2220000000022-2-200000000000000000000000000000000
χ512222-2-2-2-2222-2-222-2-222222-2-2-2-2-2-2-2-222-2-2222222-2-2222200000000-2-2-2-200000000000000000000000000000000
χ522222-2-2-2-2222-2-222-2-222222-2-2-2-2-2-2-2-222-2-22222-2-222-2-2-2-200000000222200000000000000000000000000000000
χ532222-2-2-2-222-122-2-222-2-2-1-1-1-1-1-1-11111-1-1-1-111112-2-22-1-1110000000011-1-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ542222-2-2-2-222-122-2-222-2-2-1-1-1-1-1-1-11111-1-1-1-111112-2-22-1-1110000000011-1-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ552222-2-2-2-222-122-2-222-2-2-1-1-1-1-1-1-11111-1-1-1-11111-222-211-1-100000000-1-111−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ562222-2-2-2-222-122-2-222-2-2-1-1-1-1-1-1-11111-1-1-1-11111-222-211-1-100000000-1-111i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ572222-2-2-2-222-1-2-222-2-222-1-1-111111111-1-111-1-1-1-122-2-2-1-1-1-10000000011113−3−33−333−33−3−33−333−30000000000000000
χ582222-2-2-2-222-1-2-222-2-222-1-1-111111111-1-111-1-1-1-122-2-2-1-1-1-1000000001111−333−33−3−33−333−33−3−330000000000000000
χ592222-2-2-2-222-1-2-222-2-222-1-1-111111111-1-111-1-1-1-1-2-222111100000000-1-1-1-13−3−33−333−3−333−33−3−330000000000000000
χ602222-2-2-2-222-1-2-222-2-222-1-1-111111111-1-111-1-1-1-1-2-222111100000000-1-1-1-1−333−33−3−333−3−33−333−30000000000000000
χ612-22-22-22-22-222-22-22-2-22-2-2222-2-22-22-22-22-22-22-20000000000000000000000000000000000002i−2i2i−2i000000000000
χ622-22-22-22-22-222-22-22-2-22-2-2222-2-22-22-22-22-22-22-2000000000000000000000000000000000000−2i2i−2i2i000000000000
χ632-22-22-22-22-22-22-22-222-2-2-22-2-2222-22-22-2-22-22-220000000000000000000000000000000000002i−2i−2i2i000000000000
χ642-22-22-22-22-22-22-22-222-2-2-22-2-2222-22-22-2-22-22-22000000000000000000000000000000000000−2i2i2i−2i000000000000
χ652-22-22-2-22-2222-222-22-2-2-2-22-2-2222-2-22-222-22-2-220000000000000000000000000000000000000000000000002i−2i2i−2i
χ662-22-22-2-22-2222-222-22-2-2-2-22-2-2222-2-22-222-22-2-22000000000000000000000000000000000000000000000000−2i2i−2i2i
χ672-22-22-2-22-222-22-2-22-222-2-2222-2-22-2-22-22-22-222-20000000000000000000000000000000000000000000000002-2-22
χ682-22-22-2-22-222-22-2-22-222-2-2222-2-22-2-22-22-22-222-2000000000000000000000000000000000000000000000000-222-2
χ692-22-2-222-2-2222-2-2-2-2222-2-22-2-222-222-2-222-2-222-2000000000000000000000000000000000000000000002-22-20000
χ702-22-2-222-2-2222-2-2-2-2222-2-22-2-222-222-2-222-2-222-200000000000000000000000000000000000000000000-22-220000
χ712-22-2-222-2-222-22222-2-2-2-2-2222-2-2-222-2-22-222-2-22000000000000000000000000000000000000000000002i−2i−2i2i0000
χ722-22-2-222-2-222-22222-2-2-2-2-2222-2-2-222-2-22-222-2-2200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ732-22-2-22-222-222-2-222-22-2-2-2222-2-2-22-222-22-2-22-2200000000000000000000000000000000000000002i−2i2i−2i00000000
χ742-22-2-22-222-222-2-222-22-2-2-2222-2-2-22-222-22-2-22-220000000000000000000000000000000000000000−2i2i−2i2i00000000
χ752-22-2-22-222-22-222-2-22-22-2-22-2-222-22-222-2-222-22-200000000000000000000000000000000000000002i−2i−2i2i00000000
χ762-22-2-22-222-22-222-2-22-22-2-22-2-222-22-222-2-222-22-20000000000000000000000000000000000000000−2i2i2i−2i00000000
χ774-44-44-44-44-4-24-44-44-4-4422-2-2-222-22-22-22-22-22-220000000000000000000000000000000000000000000000000000
χ784-44-44-44-44-4-2-44-44-444-422-222-2-2-22-22-222-22-22-20000000000000000000000000000000000000000000000000000
χ794-44-44-4-44-44-24-444-44-4-422-222-2-2-222-22-2-22-222-20000000000000000000000000000000000000000000000000000
χ804-44-44-4-44-44-2-44-4-44-44422-2-2-222-222-22-22-22-2-220000000000000000000000000000000000000000000000000000
χ814-44-4-444-4-44-24-4-4-4-444422-222-2-22-2-222-2-222-2-220000000000000000000000000000000000000000000000000000
χ824-44-4-444-4-44-2-44444-4-4-422-2-2-2222-2-222-22-2-222-20000000000000000000000000000000000000000000000000000
χ834-44-4-44-444-4-24-4-444-44-422-2-2-2222-22-2-22-222-22-20000000000000000000000000000000000000000000000000000
χ844-44-4-44-444-4-2-444-4-44-4422-222-2-22-22-2-222-2-22-220000000000000000000000000000000000000000000000000000
χ8588-8-80000008000000008-8-800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400000000-44443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-400000000-444−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000800000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-4000000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-4000000004-44−434343−430000000000000000000000000000000000000000000000000000000000000000

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