Finite Group Databasebeta

← Group #10824321

Character table — Group #10824321

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1222222222344444444666121212126666661212121212124444888888881212121212121212242424242424242424242424242424244444444488888888
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
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ9111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ10111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111
χ11111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-11111-1-1-1-111
χ12111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-1-1-11111-1-1
χ13111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-111-1-1-1-111-1-111
χ14111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-11111-1-111-1-1
χ15111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-1-111-1-11111-1-1
χ16111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000002i−2i2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-200000000−2i2i−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
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
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111000000002i−2i2i−2i−i3−i3i3i3−i3−i3i3i333−3−333−3−3−i−iii−i−iii0000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111000000002i−2i2i−2ii3i3−i3−i3i3i3−i3−i3−3−333−3−333−i−iii−i−iii0000000000000000
χ252222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100000000−2i2i−2i2i−i3−i3i3i3−i3−i3i3i3−3−333−3−333ii−i−iii−i−i0000000000000000
χ262222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100000000−2i2i−2i2ii3i3−i3−i3i3i3−i3−i333−3−333−3−3ii−i−iii−i−i0000000000000000
χ27222222-2-2-2-22-22222-2-2-2222222222-2-2-2-2-2-222-2-2000000002i−2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ28222222-2-2-2-22-22222-2-2-2222222222-2-2-2-2-2-222-2-200000000−2i2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
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
χ33222222-2-2-2-2-1-22222-2-2-2-1-1-1-1-1-1-1-1-1111111-1-111000000002i−2i−2i2i−i3−i3i3i3i3i3−i3−i333−3−3−3−333−i−iiiii−i−i0000000000000000
χ34222222-2-2-2-2-1-22222-2-2-2-1-1-1-1-1-1-1-1-1111111-1-111000000002i−2i−2i2ii3i3−i3−i3−i3−i3i3i3−3−33333−3−3−i−iiiii−i−i0000000000000000
χ35222222-2-2-2-2-1-22222-2-2-2-1-1-1-1-1-1-1-1-1111111-1-11100000000−2i2i2i−2i−i3−i3i3i3i3i3−i3−i3−3−33333−3−3ii−i−i−i−iii0000000000000000
χ36222222-2-2-2-2-1-22222-2-2-2-1-1-1-1-1-1-1-1-1111111-1-11100000000−2i2i2i−2ii3i3−i3−i3−i3−i3i3i333−3−3−3−333ii−i−i−i−iii0000000000000000
χ372222-2-222-2-22222-2-2-2-222222222-2-222-2-22-2-2-22-20000000000000000000000000000000000000000000000002-22-2
χ382222-2-222-2-22222-2-2-2-222222222-2-222-2-22-2-2-22-2000000000000000000000000000000000000000000000000-22-22
χ392222-2-222-2-22-2-2-22222-2222-2-2-2-2-2-222-2-2-2222-220000000000000000000000000000000000002-2-22000000000000
χ402222-2-222-2-22-2-2-22222-2222-2-2-2-2-2-222-2-2-2222-22000000000000000000000000000000000000-222-2000000000000
χ412222-2-2-2-22222-2-222-2-22222-2-2-2-2-2-2-2-2222-2222-20000000000000000000000000000000000000000000000002-2-22
χ422222-2-2-2-22222-2-222-2-22222-2-2-2-2-2-2-2-2222-2222-2000000000000000000000000000000000000000000000000-222-2
χ432222-2-2-2-2222-222-2-222-22222222-2-2-2-222-22-2-2-2200000000000000000000000000000000000022-2-2000000000000
χ442222-2-2-2-2222-222-2-222-22222222-2-2-2-222-22-2-2-22000000000000000000000000000000000000-2-222000000000000
χ4522-2-22-22-22-2222-22-22-2-22-2-222-2-22-22-22-22-22-2-2200002-22-20000000000002-22-22-22-2000000000000000000000000
χ4622-2-22-22-22-2222-22-22-2-22-2-222-2-22-22-22-22-22-2-220000-22-22000000000000-22-22-22-22000000000000000000000000
χ4722-2-22-22-22-22-2-22-22-2222-2-2-2-2222-22-22-2-22-222-22i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ4822-2-22-22-22-22-2-22-22-2222-2-2-2-2222-22-22-2-22-222-2−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ4922-2-22-22-22-2-122-22-22-2-2-111-1-111-11-11-11-11-111-100002-22-200003−3−333−3−33-11-11-11-113−33−33−33−30000000000000000
χ5022-2-22-22-22-2-122-22-22-2-2-111-1-111-11-11-11-11-111-100002-22-20000−333−3−333−3-11-11-11-11−33−33−33−330000000000000000
χ5122-2-22-22-22-2-122-22-22-2-2-111-1-111-11-11-11-11-111-10000-22-2200003−3−333−3−331-11-11-11-1−33−33−33−330000000000000000
χ5222-2-22-22-22-2-122-22-22-2-2-111-1-111-11-11-11-11-111-10000-22-220000−333−3−333−31-11-11-11-13−33−33−33−30000000000000000
χ5322-2-22-22-22-2-1-2-22-22-222-11111-1-1-11-11-111-11-1-112i−2i2i−2i00000000−ii−ii−ii−ii3−3−333−3−33i3−i3−i3i3i3−i3−i3i30000000000000000
χ5422-2-22-22-22-2-1-2-22-22-222-11111-1-1-11-11-111-11-1-112i−2i2i−2i00000000−ii−ii−ii−ii−333−3−333−3−i3i3i3−i3−i3i3i3−i30000000000000000
χ5522-2-22-22-22-2-1-2-22-22-222-11111-1-1-11-11-111-11-1-11−2i2i−2i2i00000000i−ii−ii−ii−i3−3−333−3−33−i3i3i3−i3−i3i3i3−i30000000000000000
χ5622-2-22-22-22-2-1-2-22-22-222-11111-1-1-11-11-111-11-1-11−2i2i−2i2i00000000i−ii−ii−ii−i−333−3−333−3i3−i3−i3i3i3−i3−i3i30000000000000000
χ5722-2-22-2-22-2222-22-222-2-22-2-2-2-2222-2-22-222-2-22-2200002-2-220000000000002-22-2-22-22000000000000000000000000
χ5822-2-22-2-22-2222-22-222-2-22-2-2-2-2222-2-22-222-2-22-220000-222-2000000000000-22-222-22-2000000000000000000000000
χ5922-2-22-2-22-222-22-22-2-2222-2-222-2-22-2-22-22-222-22-22i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6022-2-22-2-22-222-22-22-2-2222-2-222-2-22-2-22-22-222-22-2−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6122-2-22-2-22-22-12-22-222-2-2-11111-1-1-111-11-1-111-11-100002-2-2200003−3−33−333−3-11-111-11-13−33−3−33−330000000000000000
χ6222-2-22-2-22-22-12-22-222-2-2-11111-1-1-111-11-1-111-11-100002-2-220000−333−33−3−33-11-111-11-1−33−333−33−30000000000000000
χ6322-2-22-2-22-22-12-22-222-2-2-11111-1-1-111-11-1-111-11-10000-222-200003−3−33−333−31-11-1-11-11−33−333−33−30000000000000000
χ6422-2-22-2-22-22-12-22-222-2-2-11111-1-1-111-11-1-111-11-10000-222-20000−333−33−3−331-11-1-11-113−33−3−33−330000000000000000
χ6522-2-22-2-22-22-1-22-22-2-222-111-1-111-111-11-11-1-11-112i−2i−2i2i00000000−ii−iii−ii−i3−3−33−333−3i3−i3−i3i3−i3i3i3−i30000000000000000
χ6622-2-22-2-22-22-1-22-22-2-222-111-1-111-111-11-11-1-11-112i−2i−2i2i00000000−ii−iii−ii−i−333−33−3−33−i3i3i3−i3i3−i3−i3i30000000000000000
χ6722-2-22-2-22-22-1-22-22-2-222-111-1-111-111-11-11-1-11-11−2i2i2i−2i00000000i−ii−i−ii−ii3−3−33−333−3−i3i3i3−i3i3−i3−i3i30000000000000000
χ6822-2-22-2-22-22-1-22-22-2-222-111-1-111-111-11-11-1-11-11−2i2i2i−2i00000000i−ii−i−ii−ii−333−33−3−33i3−i3−i3i3−i3i3i3−i30000000000000000
χ6922-2-2-222-2-22222-2-22-22-22-2-222-2-2-222-2-2222-22-2-2000000000000000000000000000000000000000000002-22-20000
χ7022-2-2-222-2-22222-2-22-22-22-2-222-2-2-222-2-2222-22-2-200000000000000000000000000000000000000000000-22-220000
χ7122-2-2-222-2-222-2-222-22-222-2-2-2-222-222-2-22-2-22-22200000000000000000000000000000000000000002i−2i2i−2i00000000
χ7222-2-2-222-2-222-2-222-22-222-2-2-2-222-222-2-22-2-22-2220000000000000000000000000000000000000000−2i2i−2i2i00000000
χ7322-2-2-22-222-222-222-2-22-22-2-2-2-222-22-222-2222-2-2-2000000000000000000000000000000000000000000002-2-220000
χ7422-2-2-22-222-222-222-2-22-22-2-2-2-222-22-222-2222-2-2-200000000000000000000000000000000000000000000-222-20000
χ7522-2-2-22-222-22-22-2-222-222-2-222-2-2-22-222-2-2-2-222200000000000000000000000000000000000000002i−2i−2i2i00000000
χ7622-2-2-22-222-22-22-2-222-222-2-222-2-2-22-222-2-2-2-22220000000000000000000000000000000000000000−2i2i2i−2i00000000
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
χ8144-4-4-444-4-44-244-4-44-44-4-222-2-2222-2-222-2-2-22-2220000000000000000000000000000000000000000000000000000
χ8244-4-4-444-4-44-2-4-444-44-44-22222-2-22-2-222-222-22-2-20000000000000000000000000000000000000000000000000000
χ8344-4-4-44-444-4-24-444-4-44-4-22222-2-22-22-2-22-2-2-22220000000000000000000000000000000000000000000000000000
χ8444-4-4-44-444-4-2-44-4-444-44-222-2-2222-22-2-22222-2-2-20000000000000000000000000000000000000000000000000000
χ858-88-8000000800000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8000000-4000000004-4443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ878-88-8000000-4000000004-44−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000800000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-40000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-40000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000

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