Finite Group Databasebeta

← Group #10823677

Character table — Group #10823677

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1222223444444444444666121212126612121212121212121212224444444444666612121212121212121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-11-1-1-11-11-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111-11-1-1-11-11-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111-11-11-1-1-11-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111111111-11-11-1-1-11-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ91111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11-1-11-1-1-111-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ121111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11-1-11-1-1-111-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ131111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-111-1-1-11-1-1111-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ141111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-111-1-1-11-1-1111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ151111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-111-1-1-1-111-1-111
χ161111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-111-1-1
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-222-2-2-2-2-2-2222200002-200002-2000000000000000022-2-222-2-20000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-222-2-2-2-2-2-222220000-220000-220000000000000000-2-222-2-2220000000000000000
χ192222222-2-2-2-22222-2-2-2-222222222222-2-2-2-2-2-2-2-200002-20000-22000000000000000022-2-2-2-2220000000000000000
χ202222222-2-2-2-22222-2-2-2-222222222222-2-2-2-2-2-2-2-20000-2200002-20000000000000000-2-22222-2-20000000000000000
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
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-22-2-2-22-22-2-2-2-1-111-1-111-1-1-1-11111111111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-22-2-2-22-22-2-211-1-111-1-11111-1-1-1-1111111110000000000000000
χ24222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ25222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-1111111-1-1-1-100002-200002-2−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3-1-111-1-1110000000000000000
χ26222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-1111111-1-1-1-100002-200002-2i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3-1-111-1-1110000000000000000
χ27222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-1111111-1-1-1-10000-220000-22−i3i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3i3−i311-1-111-1-10000000000000000
χ28222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-1111111-1-1-1-10000-220000-22i3−i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3−i3i311-1-111-1-10000000000000000
χ29222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100002-20000-22−i3i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3-1-11111-1-10000000000000000
χ30222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100002-20000-22i3−i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3-1-11111-1-10000000000000000
χ31222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000-2200002-2−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i311-1-1-1-1110000000000000000
χ32222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000-2200002-2i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i311-1-1-1-1110000000000000000
χ33222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-111-1-1-1-1111122-2-222-2-222-2-2-1-1-1-11111-1-111-1-111-1-1-1-111110000000000000000
χ34222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-111-1-1-1-111112-2-22-2-2-222-222-1-11111-1-1-1-11111-1-11111-1-1-1-10000000000000000
χ35222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-111-1-1-1-11111-222-2-2-22-2-222211-1-1-1-11111-1-1-1-1111111-1-1-1-10000000000000000
χ36222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-111-1-1-1-11111-2-2222222-2-2-2-21111-1-1-1-111-1-111-1-1-1-1-1-111110000000000000000
χ372222-2-2222-2-222-2-222-2-22222222-2-2-2-222-2-222-2-2020-200020-200002200220000-2-2-2-2000000000000000000000000
χ382222-2-2222-2-222-2-222-2-22222222-2-2-2-222-2-222-2-20-202000-2020000-2-200-2-200002222000000000000000000000000
χ392222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-222-2-22222-2-2202000-20-20002200-2-200-2-2220000000000000000000000000000
χ402222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-222-2-22222-2-2-20-2000202000-2-200220022-2-20000000000000000000000000000
χ412222-2-22-2-22222-2-2-2-2222222222-2-2-2-2-2-222-2-22220-200020-200022002200-2-2-2-20000000000000000000000000000
χ422222-2-22-2-22222-2-2-2-2222222222-2-2-2-2-2-222-2-222-202000-202000-2-200-2-20022220000000000000000000000000000
χ432222-2-22-2-222-2-22222-2-2222-2-2-2-2-2-22222-2-2-2-2220202000-20-200002200-2-20000-2-222000000000000000000000000
χ442222-2-22-2-222-2-22222-2-2222-2-2-2-2-2-22222-2-2-2-2220-20-20002020000-2-20022000022-2-2000000000000000000000000
χ452222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-111020-200020-200−i3i3-1-1i3−i3-1-1i3−i3−i3i31111−i3i3−i3i3−i3i3−i3i30000000000000000
χ462222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-111020-200020-200i3−i3-1-1−i3i3-1-1−i3i3i3−i31111i3−i3i3−i3i3−i3i3−i30000000000000000
χ472222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-1110-202000-20200−i3i311i3−i311i3−i3−i3i3-1-1-1-1i3−i3i3−i3i3−i3i3−i30000000000000000
χ482222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-1110-202000-20200i3−i311−i3i311−i3i3i3−i3-1-1-1-1−i3i3−i3i3−i3i3−i3i30000000000000000
χ492222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-111-1-1-1-111202000-20-2000-1-1−i3i311−i3i311-1-1i3−i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ502222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-111-1-1-1-111202000-20-2000-1-1i3−i311i3−i311-1-1−i3i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ512222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-111-1-1-1-111-20-200020200011−i3i3-1-1−i3i3-1-111i3−i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ522222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-111-1-1-1-111-20-200020200011i3−i3-1-1i3−i3-1-111−i3i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ532222-2-2-1-2-22222-2-2-2-222-1-1-1-1-1-1-1111111-1-111-1-120-200020-2000-1-1−i3i3-1-1i3−i31111i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ542222-2-2-1-2-22222-2-2-2-222-1-1-1-1-1-1-1111111-1-111-1-120-200020-2000-1-1i3−i3-1-1−i3i31111−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ552222-2-2-1-2-22222-2-2-2-222-1-1-1-1-1-1-1111111-1-111-1-1-202000-20200011−i3i311i3−i3-1-1-1-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ562222-2-2-1-2-22222-2-2-2-222-1-1-1-1-1-1-1111111-1-111-1-1-202000-20200011i3−i311−i3i3-1-1-1-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ572222-2-2-1-2-222-2-22222-2-2-1-1-1111111-1-1-1-11111-1-10202000-20-200−i3i3-1-1−i3i311i3−i3i3−i311-1-1−i3i3−i3i3i3−i3i3−i30000000000000000
χ582222-2-2-1-2-222-2-22222-2-2-1-1-1111111-1-1-1-11111-1-10202000-20-200i3−i3-1-1i3−i311−i3i3−i3i311-1-1i3−i3i3−i3−i3i3−i3i30000000000000000
χ592222-2-2-1-2-222-2-22222-2-2-1-1-1111111-1-1-1-11111-1-10-20-200020200−i3i311−i3i3-1-1i3−i3i3−i3-1-111i3−i3i3−i3−i3i3−i3i30000000000000000
χ602222-2-2-1-2-222-2-22222-2-2-1-1-1111111-1-1-1-11111-1-10-20-200020200i3−i311i3−i3-1-1−i3i3−i3i3-1-111−i3i3−i3i3i3−i3i3−i30000000000000000
χ612-2-222-222i−2i2i−2i2i−2i2i−2i2-22-2-22-22i2i−2i−2i2-22i−2i2-22-22i−2i2i−2i0000000000000000000000000000000000000000000000002i−2i2-2
χ622-2-222-222i−2i2i−2i2i−2i2i−2i2-22-2-22-22i2i−2i−2i2-22i−2i2-22-22i−2i2i−2i000000000000000000000000000000000000000000000000−2i2i-22
χ632-2-222-222i−2i2i−2i−2i2i−2i2i-22-22-22-2−2i−2i2i2i2-2−2i2i-22-222i−2i2i−2i000000000000000000000000000000000000000000002i−2i2-20000
χ642-2-222-222i−2i2i−2i−2i2i−2i2i-22-22-22-2−2i−2i2i2i2-2−2i2i-22-222i−2i2i−2i00000000000000000000000000000000000000000000−2i2i-220000
χ652-2-222-22−2i2i−2i2i2i−2i2i−2i-22-22-22-22i2i−2i−2i2-22i−2i-22-22−2i2i−2i2i000000000000000000000000000000000000000000002i−2i-220000
χ662-2-222-22−2i2i−2i2i2i−2i2i−2i-22-22-22-22i2i−2i−2i2-22i−2i-22-22−2i2i−2i2i00000000000000000000000000000000000000000000−2i2i2-20000
χ672-2-222-22−2i2i−2i2i−2i2i−2i2i2-22-2-22-2−2i−2i2i2i2-2−2i2i2-22-2−2i2i−2i2i0000000000000000000000000000000000000000000000002i−2i-22
χ682-2-222-22−2i2i−2i2i−2i2i−2i2i2-22-2-22-2−2i−2i2i2i2-2−2i2i2-22-2−2i2i−2i2i000000000000000000000000000000000000000000000000−2i2i2-2
χ692-2-22-2222i−2i−2i2i2i−2i−2i2i2-2-22-22-22i2i−2i−2i-22−2i2i2-2-222i−2i−2i2i0000000000000000000000000000000000002i−2i2-2000000000000
χ702-2-22-2222i−2i−2i2i2i−2i−2i2i2-2-22-22-22i2i−2i−2i-22−2i2i2-2-222i−2i−2i2i000000000000000000000000000000000000−2i2i-22000000000000
χ712-2-22-2222i−2i−2i2i−2i2i2i−2i-222-2-22-2−2i−2i2i2i-222i−2i-222-22i−2i−2i2i00000000000000000000000000000000000000002-22i−2i00000000
χ722-2-22-2222i−2i−2i2i−2i2i2i−2i-222-2-22-2−2i−2i2i2i-222i−2i-222-22i−2i−2i2i0000000000000000000000000000000000000000-22−2i2i00000000
χ732-2-22-222−2i2i2i−2i2i−2i−2i2i-222-2-22-22i2i−2i−2i-22−2i2i-222-2−2i2i2i−2i00000000000000000000000000000000000000002-2−2i2i00000000
χ742-2-22-222−2i2i2i−2i2i−2i−2i2i-222-2-22-22i2i−2i−2i-22−2i2i-222-2−2i2i2i−2i0000000000000000000000000000000000000000-222i−2i00000000
χ752-2-22-222−2i2i2i−2i−2i2i2i−2i2-2-22-22-2−2i−2i2i2i-222i−2i2-2-22−2i2i2i−2i0000000000000000000000000000000000002i−2i-22000000000000
χ762-2-22-222−2i2i2i−2i−2i2i2i−2i2-2-22-22-2−2i−2i2i2i-222i−2i2-2-22−2i2i2i−2i000000000000000000000000000000000000−2i2i2-2000000000000
χ774-4-444-4-24i−4i4i−4i4i−4i4i−4i4-44-42-22−2i−2i2i2i-22−2i2i-22-22−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ784-4-444-4-24i−4i4i−4i−4i4i−4i4i-44-442-222i2i−2i−2i-222i−2i2-22-2−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ794-4-444-4-2−4i4i−4i4i4i−4i4i−4i-44-442-22−2i−2i2i2i-22−2i2i2-22-22i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ804-4-444-4-2−4i4i−4i4i−4i4i−4i4i4-44-42-222i2i−2i−2i-222i−2i-22-222i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ814-4-44-44-24i−4i−4i4i4i−4i−4i4i4-4-442-22−2i−2i2i2i2-22i−2i-222-2−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ824-4-44-44-24i−4i−4i4i−4i4i4i−4i-444-42-222i2i−2i−2i2-2−2i2i2-2-22−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ834-4-44-44-2−4i4i4i−4i4i−4i−4i4i-444-42-22−2i−2i2i2i2-22i−2i2-2-222i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ844-4-44-44-2−4i4i4i−4i−4i4i4i−4i4-4-442-222i2i−2i−2i2-2−2i2i-222-22i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ8588-8-8008000000000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-400000000000044-443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-400000000000044-4−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-88-80080000000000008-8-800000000000000000000000000000000000000000000000000000000000000000000
χ898-88-800-4000000000000-444−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ908-88-800-4000000000000-4444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000

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