Finite Group Databasebeta

← Group #10702873

Character table — Group #10702873

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222222223444444446666666666612121212121212124444888888881212121212121212242424242424242424242424242424244444444488888888
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
χ911111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ25222222-2-2-2-2222-2-22-22-22222222-2-2-2-2222-2-2-22-200000000000000000000000000000000000000002i−2i2i−2i00000000
χ26222222-2-2-2-2222-2-22-22-22222222-2-2-2-2222-2-2-22-20000000000000000000000000000000000000000−2i2i−2i2i00000000
χ27222222-2-2-2-22-2-222-22-222222222-2-2-2-2-2-2-2222-2200000000000000000000000000000000000000002i−2i−2i2i00000000
χ28222222-2-2-2-22-2-222-22-222222222-2-2-2-2-2-2-2222-220000000000000000000000000000000000000000−2i2i2i−2i00000000
χ292222-2-222-2-222-22-22-2-2222-2-2-2-2222-2-22-2-222-22-20000000000000000000000000000000000002i−2i2i−2i000000000000
χ302222-2-222-2-222-22-22-2-2222-2-2-2-2222-2-22-2-222-22-2000000000000000000000000000000000000−2i2i−2i2i000000000000
χ312222-2-222-2-22-22-22-222-222-2-2-2-2222-2-2-222-2-22-220000000000000000000000000000000000002i−2i−2i2i000000000000
χ322222-2-222-2-22-22-22-222-222-2-2-2-2222-2-2-222-2-22-22000000000000000000000000000000000000−2i2i2i−2i000000000000
χ332222-2-2-2-22222-2-2222-2-222-2-2-2-22-2-2222-2-2-2-22222-22-20000000022-2-222-2-200000000000000000000000000000000
χ342222-2-2-2-22222-2-2222-2-222-2-2-2-22-2-2222-2-2-2-2222-22-2200000000-2-222-2-22200000000000000000000000000000000
χ352222-2-2-2-2222-222-2-2-22222-2-2-2-22-2-222-22222-2-2-22-2-220000000022-2-2-2-22200000000000000000000000000000000
χ362222-2-2-2-2222-222-2-2-22222-2-2-2-22-2-222-22222-2-2-2-222-200000000-2-22222-2-200000000000000000000000000000000
χ372222-2-2-2-222-12-2-2222-2-2-1-11111-111-1-1-11111-1-1-12-22-200000000-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ382222-2-2-2-222-12-2-2222-2-2-1-11111-111-1-1-11111-1-1-12-22-200000000-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ392222-2-2-2-222-12-2-2222-2-2-1-11111-111-1-1-11111-1-1-1-22-220000000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ402222-2-2-2-222-12-2-2222-2-2-1-11111-111-1-1-11111-1-1-1-22-220000000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ412222-2-2-2-222-1-222-2-2-222-1-11111-111-1-11-1-1-1-11112-2-2200000000-1-11111-1-133−3−3−3−33333−3−3−3−3330000000000000000
χ422222-2-2-2-222-1-222-2-2-222-1-11111-111-1-11-1-1-1-11112-2-2200000000-1-11111-1-1−3−33333−3−3−3−33333−3−30000000000000000
χ432222-2-2-2-222-1-222-2-2-222-1-11111-111-1-11-1-1-1-1111-222-20000000011-1-1-1-11133−3−3−3−333−3−33333−3−30000000000000000
χ442222-2-2-2-222-1-222-2-2-222-1-11111-111-1-11-1-1-1-1111-222-20000000011-1-1-1-111−3−33333−3−333−3−3−3−3330000000000000000
χ452-2-222-22-22-22222-2-22-2-2-2-222-2-222-22-222-22-2-2-22000000000000000000000000000000000000000000002i−2i2i−2i0000
χ462-2-222-22-22-22222-2-22-2-2-2-222-2-222-22-222-22-2-2-2200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ472-2-222-22-22-22-2-2-222-222-2-222-2-222-22-2-2-22-2222-2000000000000000000000000000000000000000000002-2-220000
χ482-2-222-22-22-22-2-2-222-222-2-222-2-222-22-2-2-22-2222-200000000000000000000000000000000000000000000-222-20000
χ492-2-222-2-22-22222-22-2-2-22-2-222-2-22-22-2222-2-222-2-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ502-2-222-2-22-22222-22-2-2-22-2-222-2-22-22-2222-2-222-2-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ512-2-222-2-22-222-2-22-2222-2-2-222-2-22-22-22-2-222-2-222000000002-2-2200000000000000002-22-2-22-220000000000000000
χ522-2-222-2-22-222-2-22-2222-2-2-222-2-22-22-22-2-222-2-22200000000-222-20000000000000000-22-222-22-20000000000000000
χ532-2-222-2-22-22-122-22-2-2-2211-1-111-11-11-1-1-111-1-111000000002i−2i2i−2i−i3i3−i3i3−i3i3−i3i33−33−33−33−3−ii−ii−ii−ii0000000000000000
χ542-2-222-2-22-22-122-22-2-2-2211-1-111-11-11-1-1-111-1-111000000002i−2i2i−2ii3−i3i3−i3i3−i3i3−i3−33−33−33−33−ii−ii−ii−ii0000000000000000
χ552-2-222-2-22-22-122-22-2-2-2211-1-111-11-11-1-1-111-1-11100000000−2i2i−2i2i−i3i3−i3i3−i3i3−i3i3−33−33−33−33i−ii−ii−ii−i0000000000000000
χ562-2-222-2-22-22-122-22-2-2-2211-1-111-11-11-1-1-111-1-11100000000−2i2i−2i2ii3−i3i3−i3i3−i3i3−i33−33−33−33−3i−ii−ii−ii−i0000000000000000
χ572-2-222-2-22-22-1-2-22-2222-211-1-111-11-11-111-1-111-1-1000000002-2-22−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3-11-111-11-10000000000000000
χ582-2-222-2-22-22-1-2-22-2222-211-1-111-11-11-111-1-111-1-1000000002-2-22i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3-11-111-11-10000000000000000
χ592-2-222-2-22-22-1-2-22-2222-211-1-111-11-11-111-1-111-1-100000000-222-2−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3−i3i3−i3i31-11-1-11-110000000000000000
χ602-2-222-2-22-22-1-2-22-2222-211-1-111-11-11-111-1-111-1-100000000-222-2i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3i3−i31-11-1-11-110000000000000000
χ612-2-22-222-2-2222-222-2-22-2-2-2-2-22222-2-222-222-22-2-200002i−2i2i−2i0000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ622-2-22-222-2-2222-222-2-22-2-2-2-2-22222-2-222-222-22-2-20000−2i2i−2i2i000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ632-2-22-222-2-222-22-2-222-22-2-2-2-22222-2-22-22-2-22-22200002-2-220000000000002-2-22-222-2000000000000000000000000
χ642-2-22-222-2-222-22-2-222-22-2-2-2-22222-2-22-22-2-22-2220000-222-2000000000000-222-22-2-22000000000000000000000000
χ652-2-22-222-2-22-12-222-2-22-21111-1-1-1-111-1-11-1-11-11100002i−2i2i−2i0000−i3i3i3−i3−i3i3i3−i3−iii−i−iii−i3−3−333−3−330000000000000000
χ662-2-22-222-2-22-12-222-2-22-21111-1-1-1-111-1-11-1-11-11100002i−2i2i−2i0000i3−i3−i3i3i3−i3−i3i3−iii−i−iii−i−333−3−333−30000000000000000
χ672-2-22-222-2-22-12-222-2-22-21111-1-1-1-111-1-11-1-11-1110000−2i2i−2i2i0000−i3i3i3−i3−i3i3i3−i3i−i−iii−i−ii−333−3−333−30000000000000000
χ682-2-22-222-2-22-12-222-2-22-21111-1-1-1-111-1-11-1-11-1110000−2i2i−2i2i0000i3−i3−i3i3i3−i3−i3i3i−i−iii−i−ii3−3−333−3−330000000000000000
χ692-2-22-222-2-22-1-22-2-222-221111-1-1-1-111-11-111-11-1-100002-2-220000−i3i3i3−i3i3−i3−i3i3-111-11-1-11−i3i3i3−i3i3−i3−i3i30000000000000000
χ702-2-22-222-2-22-1-22-2-222-221111-1-1-1-111-11-111-11-1-100002-2-220000i3−i3−i3i3−i3i3i3−i3-111-11-1-11i3−i3−i3i3−i3i3i3−i30000000000000000
χ712-2-22-222-2-22-1-22-2-222-221111-1-1-1-111-11-111-11-1-10000-222-20000−i3i3i3−i3i3−i3−i3i31-1-11-111-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ722-2-22-222-2-22-1-22-2-222-221111-1-1-1-111-11-111-11-1-10000-222-20000i3−i3−i3i3−i3i3i3−i31-1-11-111-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ732-2-22-22-222-222-2-2-2-2222-2-2-2-2222-222-22-22-22-2-220000000000000000000000000000000000000000000000002-22-2
χ742-2-22-22-222-222-2-2-2-2222-2-2-2-2222-222-22-22-22-2-22000000000000000000000000000000000000000000000000-22-22
χ752-2-22-22-222-22-22222-2-2-2-2-2-2-2222-222-2-22-22-222-20000000000000000000000000000000000000000000000002i−2i−2i2i
χ762-2-22-22-222-22-22222-2-2-2-2-2-2-2222-222-2-22-22-222-2000000000000000000000000000000000000000000000000−2i2i2i−2i
χ77444444-4-4-4-4-244-4-44-44-4-2-2-2-2-2-2-22222-2-2-2222-220000000000000000000000000000000000000000000000000000
χ78444444-4-4-4-4-2-4-444-44-44-2-2-2-2-2-2-22222222-2-2-22-20000000000000000000000000000000000000000000000000000
χ794444-4-444-4-4-24-44-44-4-44-2-22222-2-2-222-222-2-22-220000000000000000000000000000000000000000000000000000
χ804444-4-444-4-4-2-44-44-444-4-2-22222-2-2-2222-2-222-22-20000000000000000000000000000000000000000000000000000
χ814-4-444-44-44-4-2444-4-44-4-422-2-222-2-22-22-2-22-2222-20000000000000000000000000000000000000000000000000000
χ824-4-444-44-44-4-2-4-4-444-44422-2-222-2-22-2222-22-2-2-220000000000000000000000000000000000000000000000000000
χ834-4-44-44-444-4-24-4-4-4-44442222-2-2-22-2-22-22-22-222-20000000000000000000000000000000000000000000000000000
χ844-4-44-44-444-4-2-44444-4-4-42222-2-2-22-2-222-22-22-2-220000000000000000000000000000000000000000000000000000
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).