Finite Group Databasebeta

← Group #10823082

Character table — Group #10823082

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1222222222344444444666121212126666661212121212124444888888881212121212121212242424242424242424242424242424242222224488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ9111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-111-1-111-1-1
χ10111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11-1-111-1-111
χ11111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-1111-1-1-1-111
χ12111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-1-1-11111-1-1
χ13111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-11-11-1-11111-1-1
χ14111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111-11-111-1-1-1-111
χ15111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11-11-1-1-111-1-111
χ16111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-11-1111-1-111-1-1
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-200002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
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
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
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
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100002i−2i2i−2i0000−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii33−3−333−3−30000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100002i−2i2i−2i0000i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii−3−333−3−3330000000000000000
χ252222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111110000−2i2i−2i2i0000−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i−3−333−3−3330000000000000000
χ262222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111110000−2i2i−2i2i0000i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i33−3−333−3−30000000000000000
χ27222222-2-2-2-22-22222-2-2-2222222222-2-2-2-2-2-222-2-200002i−2i−2i2i0000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ28222222-2-2-2-22-22222-2-2-2222222222-2-2-2-2-2-222-2-20000−2i2i2i−2i000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ29222222-2-2-2-2-12-2-2-2-2222-1-1-11111-1-11111-1-111-1-122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ30222222-2-2-2-2-12-2-2-2-2222-1-1-11111-1-11111-1-111-1-122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ31222222-2-2-2-2-12-2-2-2-2222-1-1-11111-1-11111-1-111-1-1-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ32222222-2-2-2-2-12-2-2-2-2222-1-1-11111-1-11111-1-111-1-1-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ33222222-2-2-2-2-1-22222-2-2-2-1-1-1-1-1-1-1-1-1111111-1-11100002i−2i−2i2i0000−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i33−3−3−3−3330000000000000000
χ34222222-2-2-2-2-1-22222-2-2-2-1-1-1-1-1-1-1-1-1111111-1-11100002i−2i−2i2i0000i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i−3−33333−3−30000000000000000
χ35222222-2-2-2-2-1-22222-2-2-2-1-1-1-1-1-1-1-1-1111111-1-1110000−2i2i2i−2i0000−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii−3−33333−3−30000000000000000
χ36222222-2-2-2-2-1-22222-2-2-2-1-1-1-1-1-1-1-1-1111111-1-1110000−2i2i2i−2i0000i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii33−3−3−3−3330000000000000000
χ372222-2-222-2-22222-2-2-2-222222222-2-222-2-22-2-2-22-2000000000000000000000000000000000000000022-2-200000000
χ382222-2-222-2-22222-2-2-2-222222222-2-222-2-22-2-2-22-20000000000000000000000000000000000000000-2-22200000000
χ392222-2-222-2-22-2-2-22222-2222-2-2-2-2-2-222-2-2-2222-22000000000000000000000000000000000000000000002-22-20000
χ402222-2-222-2-22-2-2-22222-2222-2-2-2-2-2-222-2-2-2222-2200000000000000000000000000000000000000000000-22-220000
χ412222-2-2-2-22222-2-222-2-22222-2-2-2-2-2-2-2-2222-2222-200000000000000000000000000000000000000002-2-2200000000
χ422222-2-2-2-22222-2-222-2-22222-2-2-2-2-2-2-2-2222-2222-20000000000000000000000000000000000000000-222-200000000
χ432222-2-2-2-2222-222-2-222-22222222-2-2-2-222-22-2-2-22000000000000000000000000000000000000000000002-2-220000
χ442222-2-2-2-2222-222-2-222-22222222-2-2-2-222-22-2-2-2200000000000000000000000000000000000000000000-222-20000
χ452-2-222-22-22-2222-22-22-2-22-2-222-2-22-22-22-22-22-2-222i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ462-2-222-22-22-2222-22-22-2-22-2-222-2-22-22-22-22-22-2-22−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ472-2-222-22-22-22-2-22-22-2222-2-2-2-2222-22-22-2-22-222-2000000002-22-200000000000000002-22-22-22-20000000000000000
χ482-2-222-22-22-22-2-22-22-2222-2-2-2-2222-22-22-2-22-222-200000000-22-220000000000000000-22-22-22-220000000000000000
χ492-2-222-22-22-2-122-22-22-2-2-111-1-111-11-11-11-11-111-12i−2i2i−2i00000000−ii−ii−ii−ii−i3i3−i3i3−i3i3−i3i33−3−333−3−330000000000000000
χ502-2-222-22-22-2-122-22-22-2-2-111-1-111-11-11-11-11-111-12i−2i2i−2i00000000−ii−ii−ii−iii3−i3i3−i3i3−i3i3−i3−333−3−333−30000000000000000
χ512-2-222-22-22-2-122-22-22-2-2-111-1-111-11-11-11-11-111-1−2i2i−2i2i00000000i−ii−ii−ii−i−i3i3−i3i3−i3i3−i3i3−333−3−333−30000000000000000
χ522-2-222-22-22-2-122-22-22-2-2-111-1-111-11-11-11-11-111-1−2i2i−2i2i00000000i−ii−ii−ii−ii3−i3i3−i3i3−i3i3−i33−3−333−3−330000000000000000
χ532-2-222-22-22-2-1-2-22-22-222-11111-1-1-11-11-111-11-1-11000000002-22-23−3−333−3−33−333−3−333−3-11-11-11-110000000000000000
χ542-2-222-22-22-2-1-2-22-22-222-11111-1-1-11-11-111-11-1-11000000002-22-2−333−3−333−33−3−333−3−33-11-11-11-110000000000000000
χ552-2-222-22-22-2-1-2-22-22-222-11111-1-1-11-11-111-11-1-1100000000-22-223−3−333−3−333−3−333−3−331-11-11-11-10000000000000000
χ562-2-222-22-22-2-1-2-22-22-222-11111-1-1-11-11-111-11-1-1100000000-22-22−333−3−333−3−333−3−333−31-11-11-11-10000000000000000
χ572-2-222-2-22-2222-22-222-2-22-2-2-2-2222-2-22-222-2-22-222i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ582-2-222-2-22-2222-22-222-2-22-2-2-2-2222-2-22-222-2-22-22−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ592-2-222-2-22-222-22-22-2-2222-2-222-2-22-2-22-22-222-22-2000000002-2-2200000000000000002-22-2-22-220000000000000000
χ602-2-222-2-22-222-22-22-2-2222-2-222-2-22-2-22-22-222-22-200000000-222-20000000000000000-22-222-22-20000000000000000
χ612-2-222-2-22-22-12-22-222-2-2-11111-1-1-111-11-1-111-11-12i−2i−2i2i00000000−ii−iii−ii−i−i3i3−i3i3i3−i3i3−i33−3−33−333−30000000000000000
χ622-2-222-2-22-22-12-22-222-2-2-11111-1-1-111-11-1-111-11-12i−2i−2i2i00000000−ii−iii−ii−ii3−i3i3−i3−i3i3−i3i3−333−33−3−330000000000000000
χ632-2-222-2-22-22-12-22-222-2-2-11111-1-1-111-11-1-111-11-1−2i2i2i−2i00000000i−ii−i−ii−ii−i3i3−i3i3i3−i3i3−i3−333−33−3−330000000000000000
χ642-2-222-2-22-22-12-22-222-2-2-11111-1-1-111-11-1-111-11-1−2i2i2i−2i00000000i−ii−i−ii−iii3−i3i3−i3−i3i3−i3i33−3−33−333−30000000000000000
χ652-2-222-2-22-22-1-22-22-2-222-111-1-111-111-11-11-1-11-11000000002-2-223−3−33−333−3−333−33−3−33-11-111-11-10000000000000000
χ662-2-222-2-22-22-1-22-22-2-222-111-1-111-111-11-11-1-11-11000000002-2-22−333−33−3−333−3−33−333−3-11-111-11-10000000000000000
χ672-2-222-2-22-22-1-22-22-2-222-111-1-111-111-11-11-1-11-1100000000-222-23−3−33−333−33−3−33−333−31-11-1-11-110000000000000000
χ682-2-222-2-22-22-1-22-22-2-222-111-1-111-111-11-11-1-11-1100000000-222-2−333−33−3−33−333−33−3−331-11-1-11-110000000000000000
χ692-2-22-222-2-22222-2-22-22-22-2-222-2-2-222-2-2222-22-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ702-2-22-222-2-22222-2-22-22-22-2-222-2-2-222-2-2222-22-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ712-2-22-222-2-222-2-222-22-222-2-2-2-222-222-2-22-2-22-2220000000000000000000000000000000000002-22-2000000000000
χ722-2-22-222-2-222-2-222-22-222-2-2-2-222-222-2-22-2-22-222000000000000000000000000000000000000-22-22000000000000
χ732-2-22-22-222-222-222-2-22-22-2-2-2-222-22-222-2222-2-2-20000000000000000000000000000000000000000000000002i−2i−2i2i
χ742-2-22-22-222-222-222-2-22-22-2-2-2-222-22-222-2222-2-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i
χ752-2-22-22-222-22-22-2-222-222-2-222-2-2-22-222-2-2-2-22220000000000000000000000000000000000002-2-22000000000000
χ762-2-22-22-222-22-22-2-222-222-2-222-2-2-22-222-2-2-2-2222000000000000000000000000000000000000-222-2000000000000
χ774444-4-444-4-4-2444-4-4-4-44-2-2-2-2-2-2-222-2-222-2222-220000000000000000000000000000000000000000000000000000
χ784444-4-444-4-4-2-4-4-44444-4-2-2-2222222-2-2222-2-2-22-20000000000000000000000000000000000000000000000000000
χ794444-4-4-4-444-24-4-444-4-44-2-2-222222222-2-2-22-2-2-220000000000000000000000000000000000000000000000000000
χ804444-4-4-4-444-2-444-4-444-4-2-2-2-2-2-2-22222-2-22-2222-20000000000000000000000000000000000000000000000000000
χ814-4-44-444-4-44-244-4-44-44-4-222-2-2222-2-222-2-2-22-2220000000000000000000000000000000000000000000000000000
χ824-4-44-444-4-44-2-4-444-44-44-22222-2-22-2-222-222-22-2-20000000000000000000000000000000000000000000000000000
χ834-4-44-44-444-4-24-444-4-44-4-22222-2-22-22-2-22-2-2-22220000000000000000000000000000000000000000000000000000
χ844-4-44-44-444-4-2-44-4-444-44-222-2-2222-22-2-22222-2-2-20000000000000000000000000000000000000000000000000000
χ8588-8-8000000800000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-4000000004-4443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-4000000004-44−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-88-8000000800000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000-40000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-88-8000000-40000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000

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