Finite Group Databasebeta

← Group #10702197

Character table — Group #10702197

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222222223444444446666666666612121212121212124444444488881212121212121212121212121212121224242424242424244444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
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
χ9111111-1-1-1-11111-1-11-1-111-1-1-1-1111-1-11111-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111-1-1-1-11111-1-11-1-111-1-1-1-1111-1-11111-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111-1-1-1-11111-1-11-1-111-1-1-1-1111-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111-1-1-1-11111-1-11-1-111-1-1-1-1111-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111-1-1-1-11111-1-11-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111-1-1-1-11111-1-11-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111-1-1-1-11111-1-11-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111−i−iiiii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111-1-1-1-11111-1-11-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111−i−iiiii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ1822222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ23222222-2-2-2-22-2-2-222-22222-2-2-2-2222-2-2-2-2-2-222220000000000000000000000000000000000000000000000002-2-22
χ24222222-2-2-2-22-2-2-222-22222-2-2-2-2222-2-2-2-2-2-22222000000000000000000000000000000000000000000000000-222-2
χ25222222-2-2-2-2-1222-2-22-2-2-1-11111-1-1-111-1-1-1-1111122-2-22i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii0000000000000000
χ26222222-2-2-2-2-1222-2-22-2-2-1-11111-1-1-111-1-1-1-1111122-2-2−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ27222222-2-2-2-2-1222-2-22-2-2-1-11111-1-1-111-1-1-1-11111-2-2222i2i−2i−2i−2i−2i2i2i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i0000000000000000
χ28222222-2-2-2-2-1222-2-22-2-2-1-11111-1-1-111-1-1-1-11111-2-222−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii0000000000000000
χ292222-2-222-2-2222-22-2-22-222-2-2-2-22-2-22222-2-222-2-2000000002i−2i2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ302222-2-222-2-2222-22-2-22-222-2-2-2-22-2-22222-2-222-2-200000000−2i2i−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ312222-2-222-2-22-2-22-222-2222-2-2-2-22-2-222-2-222-2-2220000000000000000000000000000000000002-22-2000000000000
χ322222-2-222-2-22-2-22-222-2222-2-2-2-22-2-222-2-222-2-222000000000000000000000000000000000000-22-22000000000000
χ332222-2-222-2-2-122-22-2-22-2-1-11111-111-1-1-1-111-1-111000000002i−2i2i−2i33−3−333−3−3−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii0000000000000000
χ342222-2-222-2-2-122-22-2-22-2-1-11111-111-1-1-1-111-1-111000000002i−2i2i−2i−3−333−3−333i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii0000000000000000
χ352222-2-222-2-2-122-22-2-22-2-1-11111-111-1-1-1-111-1-11100000000−2i2i−2i2i33−3−333−3−3i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i0000000000000000
χ362222-2-222-2-2-122-22-2-22-2-1-11111-111-1-1-1-111-1-11100000000−2i2i−2i2i−3−333−3−333−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i0000000000000000
χ372222-2-2-2-222222-2-22-2-222222222-2-2-2-222-2-2-2-222000000002-2-22000000000000000022-2-2-2-2220000000000000000
χ382222-2-2-2-222222-2-22-2-222222222-2-2-2-222-2-2-2-22200000000-222-20000000000000000-2-22222-2-20000000000000000
χ392222-2-2-2-2222-2-222-222-22222222-2-2-2-2-2-22222-2-20000000000000000000000000000000000002-2-22000000000000
χ402222-2-2-2-2222-2-222-222-22222222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000-222-2000000000000
χ412222-2-2-2-222-122-2-22-2-22-1-1-1-1-1-1-11111-1-11111-1-1000000002-2-22−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000000000
χ422222-2-2-2-222-122-2-22-2-22-1-1-1-1-1-1-11111-1-11111-1-1000000002-2-22i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000000000
χ432222-2-2-2-222-122-2-22-2-22-1-1-1-1-1-1-11111-1-11111-1-100000000-222-2−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000000000
χ442222-2-2-2-222-122-2-22-2-22-1-1-1-1-1-1-11111-1-11111-1-100000000-222-2i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000000000
χ4522-2-22-22-22-222-2222-2-2-2-2-222-2-222-22-22-22-22-22-22-22-200000000000000002-22-22-22-2000000000000000000000000
χ4622-2-22-22-22-222-2222-2-2-2-2-222-2-222-22-22-22-22-22-2-22-220000000000000000-22-22-22-22000000000000000000000000
χ4722-2-22-22-22-22-22-2-2-2222-2-222-2-222-22-2-22-22-22-22000000000000000000000000000000000000000000002-22-20000
χ4822-2-22-22-22-22-22-2-2-2222-2-222-2-222-22-2-22-22-22-2200000000000000000000000000000000000000000000-22-220000
χ4922-2-22-22-22-2-12-2222-2-2-211-1-111-1-11-11-11-11-11-112-22-2000000003−33−33−33−3-11-11-11-113−33−33−33−30000000000000000
χ5022-2-22-22-22-2-12-2222-2-2-211-1-111-1-11-11-11-11-11-112-22-200000000−33−33−33−33-11-11-11-11−33−33−33−330000000000000000
χ5122-2-22-22-22-2-12-2222-2-2-211-1-111-1-11-11-11-11-11-11-22-22000000003−33−33−33−31-11-11-11-1−33−33−33−330000000000000000
χ5222-2-22-22-22-2-12-2222-2-2-211-1-111-1-11-11-11-11-11-11-22-2200000000−33−33−33−331-11-11-11-13−33−33−33−30000000000000000
χ5322-2-22-2-22-2222-22-2-2-222-2-2-2-22222-2-222-22-2-22-222-2-2200000000000000002-22-2-22-22000000000000000000000000
χ5422-2-22-2-22-2222-22-2-2-222-2-2-2-22222-2-222-22-2-22-22-222-20000000000000000-22-222-22-2000000000000000000000000
χ5522-2-22-2-22-222-22-2222-2-2-2-2-2-22222-2-22-22-222-22-2000000000000000000000000000000000000000000002i−2i−2i2i0000
χ5622-2-22-2-22-222-22-2222-2-2-2-2-2-22222-2-22-22-222-22-200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ5722-2-22-2-22-22-12-22-2-2-2221111-1-1-1-111-1-11-111-11-12-2-2200000000−i3i3−i3i3i3−i3i3−i3-11-111-11-1−i3i3−i3i3i3−i3i3−i30000000000000000
χ5822-2-22-2-22-22-12-22-2-2-2221111-1-1-1-111-1-11-111-11-12-2-2200000000i3−i3i3−i3−i3i3−i3i3-11-111-11-1i3−i3i3−i3−i3i3−i3i30000000000000000
χ5922-2-22-2-22-22-12-22-2-2-2221111-1-1-1-111-1-11-111-11-1-222-200000000−i3i3−i3i3i3−i3i3−i31-11-1-11-11i3−i3i3−i3−i3i3−i3i30000000000000000
χ6022-2-22-2-22-22-12-22-2-2-2221111-1-1-1-111-1-11-111-11-1-222-200000000i3−i3i3−i3−i3i3−i3i31-11-1-11-11−i3i3−i3i3i3−i3i3−i30000000000000000
χ6122-2-2-222-2-2222-2-22-22-22-2-2-2-2222-222-22-2-222-2-2200002-22-200002-2-222-2-2200000000000000000000000000000000
χ6222-2-2-222-2-2222-2-22-22-22-2-2-2-2222-222-22-2-222-2-220000-22-220000-222-2-222-200000000000000000000000000000000
χ6322-2-2-222-2-222-222-22-22-2-2-2-2-2222-222-2-222-2-222-200000000000000000000000000000000000000002i−2i2i−2i00000000
χ6422-2-2-222-2-222-222-22-22-2-2-2-2-2222-222-2-222-2-222-20000000000000000000000000000000000000000−2i2i−2i2i00000000
χ6522-2-2-222-2-22-12-2-22-22-221111-1-1-11-1-11-111-1-111-100002-22-20000-111-1-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ6622-2-2-222-2-22-12-2-22-22-221111-1-1-11-1-11-111-1-111-100002-22-20000-111-1-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ6722-2-2-222-2-22-12-2-22-22-221111-1-1-11-1-11-111-1-111-10000-22-2200001-1-111-1-11−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ6822-2-2-222-2-22-12-2-22-22-221111-1-1-11-1-11-111-1-111-10000-22-2200001-1-111-1-11i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ6922-2-2-22-222-222-2-2-2222-2-2-222-2-22-22-222-2-22-222-200002i−2i−2i2i00002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ7022-2-2-22-222-222-2-2-2222-2-2-222-2-22-22-222-2-22-222-20000−2i2i2i−2i0000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ7122-2-2-22-222-22-2222-2-2-22-2-222-2-22-22-22-222-22-2-2200000000000000000000000000000000000000002i−2i−2i2i00000000
χ7222-2-2-22-222-22-2222-2-2-22-2-222-2-22-22-22-222-22-2-220000000000000000000000000000000000000000−2i2i2i−2i00000000
χ7322-2-2-22-222-2-12-2-2-2222-211-1-111-11-11-1-111-11-1-1100002i−2i−2i2i0000−iii−ii−i−ii−i3i3i3−i3i3−i3−i3i33−3−33−333−30000000000000000
χ7422-2-2-22-222-2-12-2-2-2222-211-1-111-11-11-1-111-11-1-1100002i−2i−2i2i0000−iii−ii−i−iii3−i3−i3i3−i3i3i3−i3−333−33−3−330000000000000000
χ7522-2-2-22-222-2-12-2-2-2222-211-1-111-11-11-1-111-11-1-110000−2i2i2i−2i0000i−i−ii−iii−i−i3i3i3−i3i3−i3−i3i3−333−33−3−330000000000000000
χ7622-2-2-22-222-2-12-2-2-2222-211-1-111-11-11-1-111-11-1-110000−2i2i2i−2i0000i−i−ii−iii−ii3−i3−i3i3−i3i3i3−i33−3−33−333−30000000000000000
χ774444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000
χ78444444-4-4-4-4-2-4-4-444-444-2-22222-2-2-2222222-2-2-2-20000000000000000000000000000000000000000000000000000
χ794444-4-444-4-4-2-4-44-444-44-2-22222-222-2-222-2-222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-4-4-444-2-4-444-444-4-2-2-2-2-2-2-2222222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ8144-4-44-44-44-4-2-44-4-4-444422-2-222-2-22-222-22-22-22-20000000000000000000000000000000000000000000000000000
χ8244-4-44-4-44-44-2-44-4444-4-42222-2-2-2-222-22-22-2-22-220000000000000000000000000000000000000000000000000000
χ8344-4-4-444-4-44-2-444-44-44-42222-2-2-22-2-222-2-222-2-220000000000000000000000000000000000000000000000000000
χ8444-4-4-44-444-4-2-4444-4-4-4422-2-222-22-22-22-2-22-222-20000000000000000000000000000000000000000000000000000
χ858-88-80000008000000008-80000-80000000000000000000000000000000000000000000000000000000000000000
χ868-88-8000000-400000000-44−4i34i3−4i34i340000000000000000000000000000000000000000000000000000000000000000
χ878-88-8000000-400000000-444i3−4i34i3−4i340000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000800000000-880000-80000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-4000000004-4−4i34i34i3−4i340000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-4000000004-44i3−4i3−4i34i340000000000000000000000000000000000000000000000000000000000000000

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