Finite Group Databasebeta

← Group #10701894

Character table — Group #10701894

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1222222222344444444666666666661212121212121212224444444444666612121212121212121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ9111111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ12111111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ13111111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ14111111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ15111111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2002-22-2000000000022-2-222-2-20000000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200-22-220000000000-2-222-2-2220000000000000000000000000000
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
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-21111-1-1-1-1-1-1-1-11111111111110000000000000000
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
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111002-22-2000000−i3−i3i3i3-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111002-22-2000000i3i3−i3−i3-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ252222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100-22-22000000−i3−i3i3i311-1-111-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ262222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100-22-22000000i3i3−i3−i311-1-111-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ27222222-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-22222002-2-22000000000022-2-2-2-2220000000000000000000000000000
χ28222222-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-2222200-222-20000000000-2-22222-2-20000000000000000000000000000
χ29222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-111112222-2-2-2-222-2-2-1-1-1-1-1-1-1-111111111-1-1-1-111110000000000000000
χ30222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-1111122-2-222-2-2-2-222-1-1-1-11111-1-1-1-111111111-1-1-1-10000000000000000
χ31222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-11111-2-222-2-222-2-2221111-1-1-1-11111-1-1-1-11111-1-1-1-10000000000000000
χ32222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-11111-2-2-2-2222222-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ33222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-1002-2-22000000−i3−i3i3i3-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ34222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-1002-2-22000000i3i3−i3−i3-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ35222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-100-222-2000000−i3−i3i3i311-1-1-1-111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ36222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-100-222-2000000i3i3−i3−i311-1-1-1-111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ372222-2-22-22-2222-2-22-22-2-2-2-2-222222-2-222-2-222-2-2000000002-22-200000000000000002-22-22-22-20000000000000000
χ382222-2-22-22-2222-2-22-22-2-2-2-2-222222-2-222-2-222-2-200000000-22-220000000000000000-22-22-22-220000000000000000
χ392222-2-22-22-22-2-222-22-22-2-2-2-222222-2-2-2-222-2-2222-200002-200002-22-2000000002-22-2000000000000000000000000
χ402222-2-22-22-22-2-222-22-22-2-2-2-222222-2-2-2-222-2-222-220000-220000-22-2200000000-22-22000000000000000000000000
χ412222-2-22-22-2-122-2-22-22-21111-1-1-1-1-111-1-111-1-111000000002-22-2−i3i3i3−i3−i3i3−i3i3−i3i3−i3i3−i3i3i3−i3-11-11-11-110000000000000000
χ422222-2-22-22-2-122-2-22-22-21111-1-1-1-1-111-1-111-1-111000000002-22-2i3−i3−i3i3i3−i3i3−i3i3−i3i3−i3i3−i3−i3i3-11-11-11-110000000000000000
χ432222-2-22-22-2-122-2-22-22-21111-1-1-1-1-111-1-111-1-11100000000-22-22−i3i3i3−i3i3−i3i3−i3i3−i3i3−i3−i3i3i3−i31-11-11-11-10000000000000000
χ442222-2-22-22-2-122-2-22-22-21111-1-1-1-1-111-1-111-1-11100000000-22-22i3−i3−i3i3−i3i3−i3i3−i3i3−i3i3i3−i3−i3i31-11-11-11-10000000000000000
χ452222-2-22-22-2-1-2-222-22-221111-1-1-1-1-11111-1-111-1-12-200002-20000-11-11−i3i3i3−i3−i3i3i3−i3-11-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ462222-2-22-22-2-1-2-222-22-221111-1-1-1-1-11111-1-111-1-12-200002-20000-11-11i3−i3−i3i3i3−i3−i3i3-11-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ472222-2-22-22-2-1-2-222-22-221111-1-1-1-1-11111-1-111-1-1-220000-2200001-11-1−i3i3i3−i3−i3i3i3−i31-11-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ482222-2-22-22-2-1-2-222-22-221111-1-1-1-1-11111-1-111-1-1-220000-2200001-11-1i3−i3−i3i3i3−i3−i3i31-11-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ492222-2-2-22-22222-2-2-22-22-2-2-2-2222-2-22222-2-2-2-222000000002-2-2200000000000000002-22-2-22-220000000000000000
χ502222-2-2-22-22222-2-2-22-22-2-2-2-2222-2-22222-2-2-2-22200000000-222-20000000000000000-22-222-22-20000000000000000
χ512222-2-2-22-222-2-2222-22-2-2-2-2-2222-2-222-2-22222-2-22-20000-2200002-22-200000000-22-22000000000000000000000000
χ522222-2-2-22-222-2-2222-22-2-2-2-2-2222-2-222-2-22222-2-2-2200002-20000-22-22000000002-22-2000000000000000000000000
χ532222-2-2-22-22-122-2-2-22-221111-1-1-111-1-1-1-11111-1-1000000002-2-22−i3i3i3−i3−i3i3−i3i3i3−i3i3−i3i3−i3−i3i3-11-111-11-10000000000000000
χ542222-2-2-22-22-122-2-2-22-221111-1-1-111-1-1-1-11111-1-1000000002-2-22i3−i3−i3i3i3−i3i3−i3−i3i3−i3i3−i3i3i3−i3-11-111-11-10000000000000000
χ552222-2-2-22-22-122-2-2-22-221111-1-1-111-1-1-1-11111-1-100000000-222-2−i3i3i3−i3i3−i3i3−i3−i3i3−i3i3i3−i3−i3i31-11-1-11-110000000000000000
χ562222-2-2-22-22-122-2-2-22-221111-1-1-111-1-1-1-11111-1-100000000-222-2i3−i3−i3i3−i3i3−i3i3i3−i3i3−i3−i3i3i3−i31-11-1-11-110000000000000000
χ572222-2-2-22-22-1-2-2222-22-21111-1-1-111-1-111-1-1-1-1112-20000-220000-11-11−i3i3i3−i3i3−i3−i3i31-11-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ582222-2-2-22-22-1-2-2222-22-21111-1-1-111-1-111-1-1-1-1112-20000-220000-11-11i3−i3−i3i3−i3i3i3−i31-11-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ592222-2-2-22-22-1-2-2222-22-21111-1-1-111-1-111-1-1-1-111-2200002-200001-11-1−i3i3i3−i3i3−i3−i3i3-11-11i3−i3−i3i3−i3i3i3−i30000000000000000
χ602222-2-2-22-22-1-2-2222-22-21111-1-1-111-1-111-1-1-1-111-2200002-200001-11-1i3−i3−i3i3−i3i3i3−i3-11-11−i3i3i3−i3i3−i3−i3i30000000000000000
χ612-2-222-222-2-222-22-22-2-2222-2-2-2-222-22-22-22-22-22-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ622-2-222-222-2-222-22-22-2-2222-2-2-2-222-22-22-22-22-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ632-2-222-222-2-22-22-22-222-222-2-2-2-222-22-2-22-22-22-22000000000000000000000000000000000000000000002i−2i2i−2i0000
χ642-2-222-222-2-22-22-22-222-222-2-2-2-222-22-2-22-22-22-2200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ652-2-222-2-2-22222-22-2-222-222-2-2-2-22-22-222-22-2-22-220000000000000000000000000000000000000000000000002-2-22
χ662-2-222-2-2-22222-22-2-222-222-2-2-2-22-22-222-22-2-22-22000000000000000000000000000000000000000000000000-222-2
χ672-2-222-2-2-2222-22-222-2-2222-2-2-2-22-22-22-22-222-22-2000000000000000000000000000000000000000000002-2-220000
χ682-2-222-2-2-2222-22-222-2-2222-2-2-2-22-22-22-22-222-22-200000000000000000000000000000000000000000000-222-20000
χ692-2-22-222-2-2222-2-2222-2-2-2-222-2-222-2-222-2-222-2-220000000000000000000000000000000000002i−2i2i−2i000000000000
χ702-2-22-222-2-2222-2-2222-2-2-2-222-2-222-2-222-2-222-2-22000000000000000000000000000000000000−2i2i−2i2i000000000000
χ712-2-22-222-2-222-222-2-2-222-2-222-2-222-2-22-222-2-222-200000000000000000000000000000000000000002-22-200000000
χ722-2-22-222-2-222-222-2-2-222-2-222-2-222-2-22-222-2-222-20000000000000000000000000000000000000000-22-2200000000
χ732-2-22-22-222-222-2-22-2-222-2-222-2-22-222-22-2-22-222-20000000000000000000000000000000000002-2-22000000000000
χ742-2-22-22-222-222-2-22-2-222-2-222-2-22-222-22-2-22-222-2000000000000000000000000000000000000-222-2000000000000
χ752-2-22-22-222-22-222-222-2-2-2-222-2-22-222-2-222-22-2-2200000000000000000000000000000000000000002i−2i−2i2i00000000
χ762-2-22-22-222-22-222-222-2-2-2-222-2-22-222-2-222-22-2-220000000000000000000000000000000000000000−2i2i2i−2i00000000
χ774-4-444-444-4-4-24-44-44-4-44-2-22222-2-22-22-22-22-22-220000000000000000000000000000000000000000000000000000
χ784-4-444-444-4-4-2-44-44-444-4-2-22222-2-22-222-22-22-22-20000000000000000000000000000000000000000000000000000
χ794-4-444-4-4-444-24-44-4-444-4-2-22222-22-22-2-22-222-22-20000000000000000000000000000000000000000000000000000
χ804-4-444-4-4-444-2-44-444-4-44-2-22222-22-22-22-22-2-22-220000000000000000000000000000000000000000000000000000
χ814-4-44-444-4-44-24-4-4444-4-422-2-222-2-222-2-222-2-222-20000000000000000000000000000000000000000000000000000
χ824-4-44-444-4-44-2-444-4-4-44422-2-222-2-222-22-2-222-2-220000000000000000000000000000000000000000000000000000
χ834-4-44-44-444-4-24-4-44-4-44422-2-222-22-2-22-222-22-2-220000000000000000000000000000000000000000000000000000
χ844-4-44-44-444-4-2-444-444-4-422-2-222-22-2-222-2-22-222-20000000000000000000000000000000000000000000000000000
χ8588-8-800000080000000000008-8-80000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400000000−4i34i3−4i34i3-4440000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-4000000004i3−4i34i3−4i3-4440000000000000000000000000000000000000000000000000000000000000000
χ888-88-80000008000000000000-88-80000000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000-400000000−4i34i34i3−4i34-440000000000000000000000000000000000000000000000000000000000000000
χ908-88-8000000-4000000004i3−4i3−4i34i34-440000000000000000000000000000000000000000000000000000000000000000

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