Finite Group Databasebeta

← Group #10702884

Character table — Group #10702884

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222222223444444446666666666612121212121212124444444444441212121212121212121212121212121212121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ172222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-10000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ212222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-222-2-2221111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-22222-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-222-2-22222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ25222222-2-2-2-2222-2-222-2-222-2-2-2-2222-2-22222-2-2-2-2000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ26222222-2-2-2-2222-2-222-2-222-2-2-2-2222-2-22222-2-2-2-200000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ27222222-2-2-2-22-2-222-2-22222-2-2-2-2222-2-2-2-2-2-22222000000002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ28222222-2-2-2-22-2-222-2-22222-2-2-2-2222-2-2-2-2-2-2222200000000−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ29222222-2-2-2-2-122-2-222-2-2-1-11111-1-1-111-1-1-1-11111000000002i−2i2i−2i33−3−333−3−3−i−iii−i−iii−i3−i3i3i3−i3−i3i3i30000000000000000
χ30222222-2-2-2-2-122-2-222-2-2-1-11111-1-1-111-1-1-1-11111000000002i−2i2i−2i−3−333−3−333−i−iii−i−iiii3i3−i3−i3i3i3−i3−i30000000000000000
χ31222222-2-2-2-2-122-2-222-2-2-1-11111-1-1-111-1-1-1-1111100000000−2i2i−2i2i33−3−333−3−3ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i30000000000000000
χ32222222-2-2-2-2-122-2-222-2-2-1-11111-1-1-111-1-1-1-1111100000000−2i2i−2i2i−3−333−3−333ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i30000000000000000
χ33222222-2-2-2-2-1-2-222-2-222-1-11111-1-1-1111111-1-1-1-1000000002i−2i−2i2i33−3−3−3−333−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i30000000000000000
χ34222222-2-2-2-2-1-2-222-2-222-1-11111-1-1-1111111-1-1-1-1000000002i−2i−2i2i−3−33333−3−3−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000000000000000
χ35222222-2-2-2-2-1-2-222-2-222-1-11111-1-1-1111111-1-1-1-100000000−2i2i2i−2i33−3−3−3−333ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i30000000000000000
χ36222222-2-2-2-2-1-2-222-2-222-1-11111-1-1-1111111-1-1-1-100000000−2i2i2i−2i−3−33333−3−3ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000000000000000
χ372222-2-222-2-222-22-22-22-222-2-2-2-22-2-22222-2-222-2-200002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ382222-2-222-2-222-22-22-22-222-2-2-2-22-2-22222-2-222-2-20000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ392222-2-222-2-22-22-22-22-2222-2-2-2-22-2-222-2-222-2-22200002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ402222-2-222-2-22-22-22-22-2222-2-2-2-22-2-222-2-222-2-2220000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ412222-2-222-2-2-12-22-22-22-2-1-11111-111-1-1-1-111-1-11100002i−2i2i−2i0000−ii−ii−ii−ii3−33−33−33−3−i3i3−i3i3−i3i3−i3i30000000000000000
χ422222-2-222-2-2-12-22-22-22-2-1-11111-111-1-1-1-111-1-11100002i−2i2i−2i0000−ii−ii−ii−ii−33−33−33−33i3−i3i3−i3i3−i3i3−i30000000000000000
χ432222-2-222-2-2-12-22-22-22-2-1-11111-111-1-1-1-111-1-1110000−2i2i−2i2i0000i−ii−ii−ii−i3−33−33−33−3i3−i3i3−i3i3−i3i3−i30000000000000000
χ442222-2-222-2-2-12-22-22-22-2-1-11111-111-1-1-1-111-1-1110000−2i2i−2i2i0000i−ii−ii−ii−i−33−33−33−33−i3i3−i3i3−i3i3−i3i30000000000000000
χ452222-2-222-2-2-1-22-22-22-22-1-11111-111-1-111-1-111-1-100002i−2i−2i2i0000−ii−iii−ii−i3−33−3−33−33−i3i3−i3i3i3−i3i3−i30000000000000000
χ462222-2-222-2-2-1-22-22-22-22-1-11111-111-1-111-1-111-1-100002i−2i−2i2i0000−ii−iii−ii−i−33−333−33−3i3−i3i3−i3−i3i3−i3i30000000000000000
χ472222-2-222-2-2-1-22-22-22-22-1-11111-111-1-111-1-111-1-10000−2i2i2i−2i0000i−ii−i−ii−ii3−33−3−33−33i3−i3i3−i3−i3i3−i3i30000000000000000
χ482222-2-222-2-2-1-22-22-22-22-1-11111-111-1-111-1-111-1-10000−2i2i2i−2i0000i−ii−i−ii−ii−33−333−33−3−i3i3−i3i3i3−i3i3−i30000000000000000
χ492222-2-2-2-22222-2-222-2-222222222-2-2-2-222-2-2-2-2222-22-20000000000000000000000002-2-222-2-220000000000000000
χ502222-2-2-2-22222-2-222-2-222222222-2-2-2-222-2-2-2-222-22-22000000000000000000000000-222-2-222-20000000000000000
χ512222-2-2-2-2222-222-2-222-22222222-2-2-2-2-2-22222-2-22-2-220000000000000000000000002-2-22-222-20000000000000000
χ522222-2-2-2-2222-222-2-222-22222222-2-2-2-2-2-22222-2-2-222-2000000000000000000000000-222-22-2-220000000000000000
χ532222-2-2-2-222-12-2-222-2-22-1-1-1-1-1-1-11111-1-11111-1-12-22-200000000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3-111-1-111-10000000000000000
χ542222-2-2-2-222-12-2-222-2-22-1-1-1-1-1-1-11111-1-11111-1-12-22-200000000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3-111-1-111-10000000000000000
χ552222-2-2-2-222-12-2-222-2-22-1-1-1-1-1-1-11111-1-11111-1-1-22-2200000000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i31-1-111-1-110000000000000000
χ562222-2-2-2-222-12-2-222-2-22-1-1-1-1-1-1-11111-1-11111-1-1-22-2200000000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i31-1-111-1-110000000000000000
χ572222-2-2-2-222-1-222-2-222-2-1-1-1-1-1-1-1111111-1-1-1-1112-2-2200000000−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3-111-11-1-110000000000000000
χ582222-2-2-2-222-1-222-2-222-2-1-1-1-1-1-1-1111111-1-1-1-1112-2-2200000000i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3-111-11-1-110000000000000000
χ592222-2-2-2-222-1-222-2-222-2-1-1-1-1-1-1-1111111-1-1-1-111-222-200000000−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i31-1-11-111-10000000000000000
χ602222-2-2-2-222-1-222-2-222-2-1-1-1-1-1-1-1111111-1-1-1-111-222-200000000i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i31-1-11-111-10000000000000000
χ612-2-222-22-22-22222-2-2-2-22-2-222-2-222-22-22-22-22-22-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ622-2-222-22-22-22222-2-2-2-22-2-222-2-222-22-22-22-22-22-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ632-2-222-22-22-22-2-2-22222-2-2-222-2-222-22-2-22-22-22-22000000000000000000000000000000000000000000002-2-220000
χ642-2-222-22-22-22-2-2-22222-2-2-222-2-222-22-2-22-22-22-2200000000000000000000000000000000000000000000-222-20000
χ652-2-222-2-22-22222-22-2-22-2-2-2-2-22222-2-222-22-2-22-2200000000000000000000000000000000000000002i−2i2i−2i00000000
χ662-2-222-2-22-22222-22-2-22-2-2-2-2-22222-2-222-22-2-22-220000000000000000000000000000000000000000−2i2i−2i2i00000000
χ672-2-222-2-22-222-2-22-222-22-2-2-2-22222-2-22-22-222-22-200000000000000000000000000000000000000002-2-2200000000
χ682-2-222-2-22-222-2-22-222-22-2-2-2-22222-2-22-22-222-22-20000000000000000000000000000000000000000-222-200000000
χ692-2-22-222-2-2222-222-22-2-2-2-2-2-2222-222-22-2-222-2-220000000000000000000000000000000000002i−2i2i−2i000000000000
χ702-2-22-222-2-2222-222-22-2-2-2-2-2-2222-222-22-2-222-2-22000000000000000000000000000000000000−2i2i−2i2i000000000000
χ712-2-22-222-2-222-22-2-22-222-2-2-2-2222-222-2-222-2-222-20000000000000000000000000000000000002-2-22000000000000
χ722-2-22-222-2-222-22-2-22-222-2-2-2-2222-222-2-222-2-222-2000000000000000000000000000000000000-222-2000000000000
χ732-2-22-22-222-222-2-2-2-2222-2-222-2-22-22-222-2-22-222-20000000000000000000000000000000000000000000000002-22-2
χ742-2-22-22-222-222-2-2-2-2222-2-222-2-22-22-222-2-22-222-2000000000000000000000000000000000000000000000000-22-22
χ752-2-22-22-222-22-22222-2-2-2-2-222-2-22-22-22-222-22-2-220000000000000000000000000000000000000000000000002i−2i−2i2i
χ762-2-22-22-222-22-22222-2-2-2-2-222-2-22-22-22-222-22-2-22000000000000000000000000000000000000000000000000−2i2i2i−2i
χ774-4-444-44-44-4-2444-4-4-4-4422-2-222-2-22-22-22-22-22-220000000000000000000000000000000000000000000000000000
χ784-4-444-44-44-4-2-4-4-44444-422-2-222-2-22-222-22-22-22-20000000000000000000000000000000000000000000000000000
χ794-4-444-4-44-44-244-44-4-44-42222-2-2-2-222-2-22-222-22-20000000000000000000000000000000000000000000000000000
χ804-4-444-4-44-44-2-4-44-444-442222-2-2-2-222-22-22-2-22-220000000000000000000000000000000000000000000000000000
χ814-4-44-444-4-44-24-444-44-4-42222-2-2-22-2-22-222-2-222-20000000000000000000000000000000000000000000000000000
χ824-4-44-444-4-44-2-44-4-44-4442222-2-2-22-2-222-2-222-2-220000000000000000000000000000000000000000000000000000
χ834-4-44-44-444-4-24-4-4-4-444422-2-222-22-22-2-222-22-2-220000000000000000000000000000000000000000000000000000
χ844-4-44-44-444-4-2-44444-4-4-422-2-222-22-22-22-2-22-222-20000000000000000000000000000000000000000000000000000
χ8588-8-80000008000000008-80000-80000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400000000-44−4i34i3−4i34i340000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-400000000-444i3−4i34i3−4i340000000000000000000000000000000000000000000000000000000000000000
χ888-88-8000000800000000-880000-80000000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000-4000000004-4−4i34i34i3−4i340000000000000000000000000000000000000000000000000000000000000000
χ908-88-8000000-4000000004-44i3−4i3−4i34i340000000000000000000000000000000000000000000000000000000000000000

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