Finite Group Databasebeta

← Group #10824907

Character table — Group #10824907

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order122222344444444444466612121212661212121212121212121224446688888888121212121212242424242424242424242424242424244444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ121111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ131111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ141111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ151111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-222-2-22222-2-2-2-200000000002i−2i2i−2i000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-222-2-22222-2-2-2-20000000000−2i2i−2i2i00000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ192222222-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2-2-2-2-2222200000000002i−2i−2i2i000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ202222222-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2-2-2-2-222220000000000−2i2i2i−2i00000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ21222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2112222-2-2-2-2111111-1-1-1-1-1-1-1-1111111110000000000000000
χ24222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-2222211111111111111-1-1-1-1-1-1-1-10000000000000000
χ25222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-111110000−i3i300002i−2i2i−2i−i3i3−i3−i3i3i333−3−333−3−3−i−iii−i−iii0000000000000000
χ26222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-111110000−i3i30000−2i2i−2i2i−i3i3−i3−i3i3i3−3−333−3−333ii−i−iii−i−i0000000000000000
χ27222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-111110000i3−i300002i−2i2i−2ii3−i3i3i3−i3−i3−3−333−3−333−i−iii−i−iii0000000000000000
χ28222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-111110000i3−i30000−2i2i−2i2ii3−i3i3i3−i3−i333−3−333−3−3ii−i−iii−i−i0000000000000000
χ29222222-1-2-2-2-22222-2-2-2-2-1-1-11111-1-1111111-1-1-1-10000−i3i300002i−2i−2i2i−i3i3i3i3−i3−i333−3−3−3−333−i−iiiii−i−i0000000000000000
χ30222222-1-2-2-2-22222-2-2-2-2-1-1-11111-1-1111111-1-1-1-10000−i3i30000−2i2i2i−2i−i3i3i3i3−i3−i3−3−33333−3−3ii−i−i−i−iii0000000000000000
χ31222222-1-2-2-2-22222-2-2-2-2-1-1-11111-1-1111111-1-1-1-10000i3−i300002i−2i−2i2ii3−i3−i3−i3i3i3−3−33333−3−3−i−iiiii−i−i0000000000000000
χ32222222-1-2-2-2-22222-2-2-2-2-1-1-11111-1-1111111-1-1-1-10000i3−i30000−2i2i2i−2ii3−i3−i3−i3i3i333−3−3−3−333ii−i−i−i−iii0000000000000000
χ33222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1111111112-2-22-1-122-2-222-2-2-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ34222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1111111112-2-22-1-1-2-222-2-222-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ35222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-111111111-222-21122-2-2-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ36222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-111111111-222-211-2-22222-2-211-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ372222-2-2222-2-222-2-222-2-22222222-2-2-2-222-2-222-2-20000002-22-200000000002-22-22-22-2000000000000000000000000
χ382222-2-2222-2-222-2-222-2-22222222-2-2-2-222-2-222-2-2000000-22-220000000000-22-22-22-22000000000000000000000000
χ392222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-22222-2-2-2-22222-2-22200000000-2-22-22-200000000000000000000000000000000
χ402222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-22222-2-2-2-222-2-222-2-20000000022-22-2200000000000000000000000000000000
χ412222-2-22-2-22222-2-2-2-222222-2-2-2-2-2-222-2-22222-2-22-22-22200000000-2-2-22-2200000000000000000000000000000000
χ422222-2-22-2-22222-2-2-2-222222-2-2-2-2-2-222-2-22222-2-2-22-22-2-200000000222-22-200000000000000000000000000000000
χ432222-2-22-2-222-2-22222-2-22222222-2-2-2-2-2-222-2-2220000002-2-2200000000002-22-2-22-22000000000000000000000000
χ442222-2-22-2-222-2-22222-2-22222222-2-2-2-2-2-222-2-222000000-222-20000000000-22-222-22-2000000000000000000000000
χ452222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-1110000−i3i32-22-20000i3−i3−i3i3i3−i3-11-11-11-11−i3i3−i3i3−i3i3−i3i30000000000000000
χ462222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-1110000−i3i3-22-220000i3−i3−i3i3i3−i31-11-11-11-1i3−i3i3−i3i3−i3i3−i30000000000000000
χ472222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-1110000i3−i32-22-20000−i3i3i3−i3−i3i3-11-11-11-11i3−i3i3−i3i3−i3i3−i30000000000000000
χ482222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-1110000i3−i3-22-220000−i3i3i3−i3−i3i31-11-11-11-1−i3i3−i3i3−i3i3−i3i30000000000000000
χ492222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-1-1-11111-1-122-2-2-1-10000000011-11-113−3−333−3−333−3−333−3−330000000000000000
χ502222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-1-1-11111-1-122-2-2-1-10000000011-11-11−333−3−333−3−333−3−333−30000000000000000
χ512222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-1-1-11111-1-1-2-2221100000000-1-11-11-13−3−333−3−33−333−3−333−30000000000000000
χ522222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-1-1-11111-1-1-2-2221100000000-1-11-11-1−333−3−333−33−3−333−3−330000000000000000
χ532222-2-2-1-2-22222-2-2-2-222-1-1-1111111-1-111-1-1-1-1112-22-2-1-100000000111-11-13−3−33−333−33−3−33−333−30000000000000000
χ542222-2-2-1-2-22222-2-2-2-222-1-1-1111111-1-111-1-1-1-1112-22-2-1-100000000111-11-1−333−33−3−33−333−33−3−330000000000000000
χ552222-2-2-1-2-22222-2-2-2-222-1-1-1111111-1-111-1-1-1-111-22-221100000000-1-1-11-113−3−33−333−3−333−33−3−330000000000000000
χ562222-2-2-1-2-22222-2-2-2-222-1-1-1111111-1-111-1-1-1-111-22-221100000000-1-1-11-11−333−33−3−333−3−33−333−30000000000000000
χ572222-2-2-1-2-222-2-22222-2-2-1-1-1-1-1-1-1111111-1-111-1-10000−i3i32-2-220000i3−i3i3−i3−i3i3-11-111-11-1−i3i3−i3i3i3−i3i3−i30000000000000000
χ582222-2-2-1-2-222-2-22222-2-2-1-1-1-1-1-1-1111111-1-111-1-10000−i3i3-222-20000i3−i3i3−i3−i3i31-11-1-11-11i3−i3i3−i3−i3i3−i3i30000000000000000
χ592222-2-2-1-2-222-2-22222-2-2-1-1-1-1-1-1-1111111-1-111-1-10000i3−i32-2-220000−i3i3−i3i3i3−i3-11-111-11-1i3−i3i3−i3−i3i3−i3i30000000000000000
χ602222-2-2-1-2-222-2-22222-2-2-1-1-1-1-1-1-1111111-1-111-1-10000i3−i3-222-20000−i3i3−i3i3i3−i31-11-1-11-11−i3i3−i3i3i3−i3i3−i30000000000000000
χ612-2-222-222i−2i2i−2i2i−2i2i−2i2-22-22-2-222-2-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000002i−2i002-200000000
χ622-2-222-222i−2i2i−2i2i−2i2i−2i2-22-22-2-222-2-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000−2i2i00-2200000000
χ632-2-222-222i−2i2i−2i−2i2i−2i2i-22-222-2-2-2-2222-2-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000002i−2i2-20000
χ642-2-222-222i−2i2i−2i−2i2i−2i2i-22-222-2-2-2-2222-2-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000−2i2i-220000
χ652-2-222-22−2i2i−2i2i2i−2i2i−2i-22-222-2-2-2-2222-2-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000002i−2i-220000
χ662-2-222-22−2i2i−2i2i2i−2i2i−2i-22-222-2-2-2-2222-2-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000−2i2i2-20000
χ672-2-222-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000002i−2i00-2200000000
χ682-2-222-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000−2i2i002-200000000
χ692-2-22-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-222-2-2-22-222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000002i−2i002-20000000000
χ702-2-22-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-222-2-2-22-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000−2i2i00-220000000000
χ712-2-22-2222i−2i−2i2i−2i2i2i−2i-222-22-2-2-2-222-222-22i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000000000002i−2i2-2
χ722-2-22-2222i−2i−2i2i−2i2i2i−2i-222-22-2-2-2-222-222-22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000000000000000−2i2i-22
χ732-2-22-222−2i2i2i−2i2i−2i−2i2i-222-22-2-2-2-222-222-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000000000002i−2i-22
χ742-2-22-222−2i2i2i−2i2i−2i−2i2i-222-22-2-2-2-222-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000000000000000−2i2i2-2
χ752-2-22-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-222-2-2-22-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000002i−2i00-220000000000
χ762-2-22-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-222-2-2-22-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000−2i2i002-20000000000
χ774-4-444-4-24i−4i4i−4i4i−4i4i−4i4-44-4-222-2-222-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ784-4-444-4-24i−4i4i−4i−4i4i−4i4i-44-44-22222-2-2-222-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ794-4-444-4-2−4i4i−4i4i4i−4i4i−4i-44-44-22222-2-2-222-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ804-4-444-4-2−4i4i−4i4i−4i4i−4i4i4-44-4-222-2-222-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ814-4-44-44-24i−4i−4i4i4i−4i−4i4i4-4-44-222-2-2222-22-2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ824-4-44-44-24i−4i−4i4i−4i4i4i−4i-444-4-22222-2-22-2-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ834-4-44-44-2−4i4i4i−4i4i−4i−4i4i-444-4-22222-2-22-2-222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ844-4-44-44-2−4i4i4i−4i−4i4i4i−4i4-4-44-222-2-2222-22-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ8588-8-8008000000000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-40000000000004-4443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-40000000000004-44−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-88-8008000000000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ898-88-800-400000000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-88-800-400000000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000

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