Finite Group Databasebeta

← Group #10824900

Character table — Group #10824900

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222234444444444446661212121266121212121212121212128888888888882424242424242424242424242424242424242424242424242222244444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-111-1-111-1-1-1-1
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-11-1-111-1-11111
χ91111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1
χ101111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-1-1-111-1-111
χ121111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-11111-1-111-1-1
χ131111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1
χ141111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111
χ151111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-111-1-1-111-1-1-1-111
χ161111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11-1-1111-1-11111-1-1
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ192222222-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2-2-22222-2-20000000000000000000000000000000000000000000000002i−2i−2i2i
χ202222222-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i
χ21222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ24222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ25222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-111111111-1-122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ26222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-111111111-1-122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ27222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-111111111-1-1-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ28222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-111111111-1-1-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ292222-2-2222-2-222-2-222-2-22222222-2-222-2-222-2-2-2-200000000000000000000000000000000000000200-2002-2000000
χ302222-2-2222-2-222-2-222-2-22222222-2-222-2-222-2-2-2-200000000000000000000000000000000000000-200200-22000000
χ312222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-222-2-2-2-22222000000002-22-2000000000000000022-2-222-2-20000000000000000
χ322222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-222-2-2-2-2222200000000-22-220000000000000000-2-222-2-2220000000000000000
χ332222-2-22-2-22222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-222000000002-2-22000000000000000022-2-2-2-2220000000000000000
χ342222-2-22-2-22222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-22200000000-222-20000000000000000-2-22222-2-20000000000000000
χ352222-2-22-2-222-2-22222-2-22222222-2-2-2-222-2-222-2-200000000000000000000000000000000000000200-200-22000000
χ362222-2-22-2-222-2-22222-2-22222222-2-2-2-222-2-222-2-200000000000000000000000000000000000000-2002002-2000000
χ372222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-11111-1-1-1-1000000002-22-233−3−333−3−333−3−333−3−3-1-111-1-1110000000000000000
χ382222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-11111-1-1-1-1000000002-22-2−3−333−3−333−3−333−3−333-1-111-1-1110000000000000000
χ392222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-11111-1-1-1-100000000-22-2233−3−333−3−3−3−333−3−33311-1-111-1-10000000000000000
χ402222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-11111-1-1-1-100000000-22-22−3−333−3−33333−3−333−3−311-1-111-1-10000000000000000
χ412222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-1000000002-2-2233−3−3−3−33333−3−3−3−333-1-11111-1-10000000000000000
χ422222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-1000000002-2-22−3−33333−3−3−3−33333−3−3-1-11111-1-10000000000000000
χ432222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-100000000-222-233−3−3−3−333−3−33333−3−311-1-1-1-1110000000000000000
χ442222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-100000000-222-2−3−33333−3−333−3−3−3−33311-1-1-1-1110000000000000000
χ4522-2-22-222i−2i2i−2i2i−2i2i−2i2-22-22-2-222-2-22-22i−2i2i−2i2i−2i2i−2i2-20000000000000000000000000000000000002-200002i−2i00000000
χ4622-2-22-222i−2i2i−2i2i−2i2i−2i2-22-22-2-222-2-22-22i−2i2i−2i2i−2i2i−2i2-2000000000000000000000000000000000000-220000−2i2i00000000
χ4722-2-22-222i−2i2i−2i−2i2i−2i2i-22-222-2-2-2-2222-22i−2i2i−2i−2i2i−2i2i-2200002-22i−2i0000000000002-22-22i−2i2i−2i000000000000000000000000
χ4822-2-22-222i−2i2i−2i−2i2i−2i2i-22-222-2-2-2-2222-22i−2i2i−2i−2i2i−2i2i-220000-22−2i2i000000000000-22-22−2i2i−2i2i000000000000000000000000
χ4922-2-22-22−2i2i−2i2i2i−2i2i−2i-22-222-2-2-2-2222-2−2i2i−2i2i2i−2i2i−2i-2200002-2−2i2i0000000000002-22-2−2i2i−2i2i000000000000000000000000
χ5022-2-22-22−2i2i−2i2i2i−2i2i−2i-22-222-2-2-2-2222-2−2i2i−2i2i2i−2i2i−2i-220000-222i−2i000000000000-22-222i−2i2i−2i000000000000000000000000
χ5122-2-22-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-222-2-22-2−2i2i−2i2i−2i2i−2i2i2-20000000000000000000000000000000000002-20000−2i2i00000000
χ5222-2-22-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-222-2-22-2−2i2i−2i2i−2i2i−2i2i2-2000000000000000000000000000000000000-2200002i−2i00000000
χ5322-2-22-2-12i−2i2i−2i−2i2i−2i2i-22-22-11111-1-1-11−ii−iii−ii−i1-100002-22i−2i00003−33−3−i3i3−i3i3-11-11−ii−ii3−33−3−i3i3−i3i30000000000000000
χ5422-2-22-2-12i−2i2i−2i−2i2i−2i2i-22-22-11111-1-1-11−ii−iii−ii−i1-100002-22i−2i0000−33−33i3−i3i3−i3-11-11−ii−ii−33−33i3−i3i3−i30000000000000000
χ5522-2-22-2-12i−2i2i−2i−2i2i−2i2i-22-22-11111-1-1-11−ii−iii−ii−i1-10000-22−2i2i00003−33−3−i3i3−i3i31-11-1i−ii−i−33−33i3−i3i3−i30000000000000000
χ5622-2-22-2-12i−2i2i−2i−2i2i−2i2i-22-22-11111-1-1-11−ii−iii−ii−i1-10000-22−2i2i0000−33−33i3−i3i3−i31-11-1i−ii−i3−33−3−i3i3−i3i30000000000000000
χ5722-2-22-2-1−2i2i−2i2i2i−2i2i−2i-22-22-11111-1-1-11i−ii−i−ii−ii1-100002-2−2i2i00003−33−3i3−i3i3−i3-11-11i−ii−i3−33−3i3−i3i3−i30000000000000000
χ5822-2-22-2-1−2i2i−2i2i2i−2i2i−2i-22-22-11111-1-1-11i−ii−i−ii−ii1-100002-2−2i2i0000−33−33−i3i3−i3i3-11-11i−ii−i−33−33−i3i3−i3i30000000000000000
χ5922-2-22-2-1−2i2i−2i2i2i−2i2i−2i-22-22-11111-1-1-11i−ii−i−ii−ii1-10000-222i−2i00003−33−3i3−i3i3−i31-11-1−ii−ii−33−33−i3i3−i3i30000000000000000
χ6022-2-22-2-1−2i2i−2i2i2i−2i2i−2i-22-22-11111-1-1-11i−ii−i−ii−ii1-10000-222i−2i0000−33−33−i3i3−i3i31-11-1−ii−ii3−33−3i3−i3i3−i30000000000000000
χ6122-2-2-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-222-2-2-222i−2i−2i2i2i−2i−2i2i-222-22i−2i000000002-2-22−2i2i2i−2i00000000000000000000000000000000
χ6222-2-2-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-222-2-2-222i−2i−2i2i2i−2i−2i2i-22-22−2i2i00000000-222-22i−2i−2i2i00000000000000000000000000000000
χ6322-2-2-2222i−2i−2i2i−2i2i2i−2i-222-22-2-2-2-222-222i−2i−2i2i−2i2i2i−2i2-20000000000000000000000000000000000000002-2000002i−2i0000
χ6422-2-2-2222i−2i−2i2i−2i2i2i−2i-222-22-2-2-2-222-222i−2i−2i2i−2i2i2i−2i2-2000000000000000000000000000000000000000-2200000−2i2i0000
χ6522-2-2-222−2i2i2i−2i2i−2i−2i2i-222-22-2-2-2-222-22−2i2i2i−2i2i−2i−2i2i2-20000000000000000000000000000000000000002-200000−2i2i0000
χ6622-2-2-222−2i2i2i−2i2i−2i−2i2i-222-22-2-2-2-222-22−2i2i2i−2i2i−2i−2i2i2-2000000000000000000000000000000000000000-22000002i−2i0000
χ6722-2-2-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-222-2-2-22−2i2i2i−2i−2i2i2i−2i-222-2−2i2i000000002-2-222i−2i−2i2i00000000000000000000000000000000
χ6822-2-2-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-222-2-2-22−2i2i2i−2i−2i2i2i−2i-22-222i−2i00000000-222-2−2i2i2i−2i00000000000000000000000000000000
χ6922-2-2-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111-1-1111-1−iii−i−iii−i1-12-22i−2i00000000-111-1i−i−ii3−3−33i3−i3−i3i3−333−3i3−i3−i3i30000000000000000
χ7022-2-2-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111-1-1111-1−iii−i−iii−i1-12-22i−2i00000000-111-1i−i−ii−333−3−i3i3i3−i33−3−33−i3i3i3−i30000000000000000
χ7122-2-2-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111-1-1111-1−iii−i−iii−i1-1-22−2i2i000000001-1-11−iii−i3−3−33i3−i3−i3i33−3−33−i3i3i3−i30000000000000000
χ7222-2-2-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111-1-1111-1−iii−i−iii−i1-1-22−2i2i000000001-1-11−iii−i−333−3−i3i3i3−i3−333−3i3−i3−i3i30000000000000000
χ7322-2-2-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111-1-1111-1i−i−iii−i−ii1-12-2−2i2i00000000-111-1−iii−i3−3−33−i3i3i3−i3−333−3−i3i3i3−i30000000000000000
χ7422-2-2-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111-1-1111-1i−i−iii−i−ii1-12-2−2i2i00000000-111-1−iii−i−333−3i3−i3−i3i33−3−33i3−i3−i3i30000000000000000
χ7522-2-2-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111-1-1111-1i−i−iii−i−ii1-1-222i−2i000000001-1-11i−i−ii3−3−33−i3i3i3−i33−3−33i3−i3−i3i30000000000000000
χ7622-2-2-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111-1-1111-1i−i−iii−i−ii1-1-222i−2i000000001-1-11i−i−ii−333−3i3−i3−i3i3−333−3−i3i3i3−i30000000000000000
χ77444444-24444-4-4-4-4-4-4-4-4-2-2-22222-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000000
χ78444444-2-4-4-4-44444-4-4-4-4-2-2-22222-2-22222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ794444-4-4-244-4-444-4-444-4-4-2-2-2-2-2-2-222-2-222-2-222220000000000000000000000000000000000000000000000000000
χ804444-4-4-2-4-444-4-44444-4-4-2-2-2-2-2-2-22222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ8144-4-44-4-24i−4i4i−4i4i−4i4i−4i4-44-4-222-2-222-22−2i2i−2i2i−2i2i−2i2i-220000000000000000000000000000000000000000000000000000
χ8244-4-44-4-2−4i4i−4i4i−4i4i−4i4i4-44-4-222-2-222-222i−2i2i−2i2i−2i2i−2i-220000000000000000000000000000000000000000000000000000
χ8344-4-4-44-24i−4i−4i4i−4i4i4i−4i-444-4-22222-2-22-2−2i2i2i−2i2i−2i−2i2i-220000000000000000000000000000000000000000000000000000
χ8444-4-4-44-2−4i4i4i−4i4i−4i−4i4i-444-4-22222-2-22-22i−2i−2i2i−2i2i2i−2i-220000000000000000000000000000000000000000000000000000
χ858-88-8008000000000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-40000000000004-4443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ878-88-800-40000000000004-44−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8-88008000000000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-8800-400000000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8-8800-400000000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000

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