Finite Group Databasebeta

← Group #10702814

Character table — Group #10702814

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order122222222234444444466666666666121212121212121222224444666666668888121212121212121224242424242424244444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91-1-11111-1-1-1111-1-1-111-111-1-11-1-111-1-11111-1-1-1-111-1-1ii−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-111-1-1
χ101-1-11111-1-1-1111-1-1-111-111-1-11-1-111-1-11111-1-1-1-111-1-1ii−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-111
χ111-1-11111-1-1-1111-1-1-111-111-1-11-1-111-1-11111-1-1-1-111-1-1−i−iii1111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111
χ121-1-11111-1-1-1111-1-1-111-111-1-11-1-111-1-11111-1-1-1-111-1-1−i−iii1111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1
χ131-1-11111-1-1-1111-1-1-111-111-1-11-1-111-1-11111-1-1-1-1-1-111ii−i−i-1-1-1-11111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111
χ141-1-11111-1-1-1111-1-1-111-111-1-11-1-111-1-11111-1-1-1-1-1-111ii−i−i-1-1-1-11111−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1
χ151-1-11111-1-1-1111-1-1-111-111-1-11-1-111-1-11111-1-1-1-1-1-111−i−iii-1-1-1-11111ii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-11111-1-1
χ161-1-11111-1-1-1111-1-1-111-111-1-11-1-111-1-11111-1-1-1-1-1-111−i−iii-1-1-1-11111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ1822222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-211111111111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211111111-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111222211111111-1-1-1-1-1-1-1-10000000000000000
χ2322222-2-22-2-222-22-222-2-2-2-2222-2-22-22-222-2-22-2-220000000000000000000000000000000000002i−2i2i−2i000000000000
χ2422222-2-22-2-222-22-222-2-2-2-2222-2-22-22-222-2-22-2-22000000000000000000000000000000000000−2i2i−2i2i000000000000
χ2522222-2-22-2-22-22-22-2-222-2-2222-2-22-22-2-2-222-222-200000000000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222-2-22-2-22-22-22-2-222-2-2222-2-22-22-2-2-222-222-20000000000000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222-2-22-2-2-1-22-22-2-22211-1-1-111-11-1111-1-11-1-1100000000−i3−i3i3i3−i3−i3i3i32i−2i2i−2i33−3−333−3−3−i−iii−i−iii0000000000000000
χ2822222-2-22-2-2-1-22-22-2-22211-1-1-111-11-1111-1-11-1-1100000000−i3−i3i3i3−i3−i3i3i3−2i2i−2i2i−3−333−3−333ii−i−iii−i−i0000000000000000
χ2922222-2-22-2-2-1-22-22-2-22211-1-1-111-11-1111-1-11-1-1100000000i3i3−i3−i3i3i3−i3−i32i−2i2i−2i−3−333−3−333−i−iii−i−iii0000000000000000
χ3022222-2-22-2-2-1-22-22-2-22211-1-1-111-11-1111-1-11-1-1100000000i3i3−i3−i3i3i3−i3−i3−2i2i−2i2i33−3−333−3−3ii−i−iii−i−i0000000000000000
χ312222-22-2-22-22222-2-2-2-222222222-2-2-2-22-22-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ322222-22-2-22-22222-2-2-2-222222222-2-2-2-22-22-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ332222-22-2-22-22-2-2-22222-22222222-2-2-2-2-22-22-2-2222-22-200002-22-22-22-2000000000000000000000000000000000000
χ342222-22-2-22-22-2-2-22222-22222222-2-2-2-2-22-22-2-222-22-220000-22-22-22-22000000000000000000000000000000000000
χ352222-22-2-22-2-1-2-2-22222-2-1-1-1-1-1-1-111111-11-111-1-12-22-20000-11-11-11-110000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ362222-22-2-22-2-1-2-2-22222-2-1-1-1-1-1-1-111111-11-111-1-12-22-20000-11-11-11-110000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ372222-22-2-22-2-1-2-2-22222-2-1-1-1-1-1-1-111111-11-111-1-1-22-2200001-11-11-11-10000−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ382222-22-2-22-2-1-2-2-22222-2-1-1-1-1-1-1-111111-11-111-1-1-22-2200001-11-11-11-10000i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ392222-2-22-2-2222-222-2-22-2-2-2222-2-2-22-222-2-222-22-200002i−2i2i−2i0000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ402222-2-22-2-2222-222-2-22-2-2-2222-2-2-22-222-2-222-22-20000−2i2i−2i2i000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ412222-2-22-2-222-22-2-222-22-2-2222-2-2-22-22-222-2-22-2200000000000000000000000000000000000000002-22-200000000
χ422222-2-22-2-222-22-2-222-22-2-2222-2-2-22-22-222-2-22-220000000000000000000000000000000000000000-22-2200000000
χ432222-2-22-2-22-12-222-2-22-211-1-1-1111-11-1-111-1-11-1100002i−2i2i−2i−i3i3i3−i3−i3i3i3−i30000−iii−i−iii−i3−3−333−3−330000000000000000
χ442222-2-22-2-22-12-222-2-22-211-1-1-1111-11-1-111-1-11-1100002i−2i2i−2ii3−i3−i3i3i3−i3−i3i30000−iii−i−iii−i−333−3−333−30000000000000000
χ452222-2-22-2-22-12-222-2-22-211-1-1-1111-11-1-111-1-11-110000−2i2i−2i2i−i3i3i3−i3−i3i3i3−i30000i−i−iii−i−ii−333−3−333−30000000000000000
χ462222-2-22-2-22-12-222-2-22-211-1-1-1111-11-1-111-1-11-110000−2i2i−2i2ii3−i3−i3i3i3−i3−i3i30000i−i−iii−i−ii3−3−333−3−330000000000000000
χ472-2-22222-2-2-22-2-2222-2-2222-2-22-2-222-2-2-2-2-2-222220000000000000000000000000000000000000000000000002i−2i−2i2i
χ482-2-22222-2-2-22-2-2222-2-2222-2-22-2-222-2-2-2-2-2-22222000000000000000000000000000000000000000000000000−2i2i2i−2i
χ492-2-22222-2-2-2-122-2-2-222-2-1-111-111-1-111-1-1-1-1111122-2-22i2i−2i−2i-1-1-1-111112i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ502-2-22222-2-2-2-122-2-2-222-2-1-111-111-1-111-1-1-1-1111122-2-2−2i−2i2i2i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ512-2-22222-2-2-2-122-2-2-222-2-1-111-111-1-111-1-1-1-11111-2-2222i2i−2i−2i1111-1-1-1-1−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ522-2-22222-2-2-2-122-2-2-222-2-1-111-111-1-111-1-1-1-11111-2-222−2i−2i2i2i1111-1-1-1-12i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ532-2-222-2-2-22222-2-22-22-22-2-2-2-22222-2-2222-2-2-222-20000000000000000000000000000000000002-2-22000000000000
χ542-2-222-2-2-22222-2-22-22-22-2-2-2-22222-2-2222-2-2-222-2000000000000000000000000000000000000-222-2000000000000
χ552-2-222-2-2-2222-222-22-22-2-2-2-2-22222-2-22-2-2222-2-2200000000000000002-2-220000000022-2-2-2-2220000000000000000
χ562-2-222-2-2-2222-222-22-22-2-2-2-2-22222-2-22-2-2222-2-220000000000000000-222-200000000-2-22222-2-20000000000000000
χ572-2-222-2-2-222-1-222-22-22-21111-1-1-1-111-111-1-1-111-100000000−i3−i3i3i3i3i3−i3−i32-2-22−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000000000
χ582-2-222-2-2-222-1-222-22-22-21111-1-1-1-111-111-1-1-111-100000000−i3−i3i3i3i3i3−i3−i3-222-2i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000000000
χ592-2-222-2-2-222-1-222-22-22-21111-1-1-1-111-111-1-1-111-100000000i3i3−i3−i3−i3−i3i3i32-2-22i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000000000
χ602-2-222-2-2-222-1-222-22-22-21111-1-1-1-111-111-1-1-111-100000000i3i3−i3−i3−i3−i3i3i3-222-2−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000000000
χ612-2-22-22-22-22222-222-2-2-222-2-22-2-2-2-2222-22-2-2-222000000000000000000000000000000000000000000002i−2i−2i2i0000
χ622-2-22-22-22-22222-222-2-2-222-2-22-2-2-2-2222-22-2-2-22200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ632-2-22-22-22-222-2-22-2-222222-2-22-2-2-2-222-22-2222-2-22-2-2200002-22-2-22-22000000000000000000000000000000000000
χ642-2-22-22-22-222-2-22-2-222222-2-22-2-2-2-222-22-2222-2-2-222-20000-22-222-22-2000000000000000000000000000000000000
χ652-2-22-22-22-22-1-2-22-2-2222-1-111-11111-1-11-11-1-1-1112-2-220000-11-111-11-100003−33−3−33−333−33−3−33−330000000000000000
χ662-2-22-22-22-22-1-2-22-2-2222-1-111-11111-1-11-11-1-1-1112-2-220000-11-111-11-10000−33−333−33−3−33−333−33−30000000000000000
χ672-2-22-22-22-22-1-2-22-2-2222-1-111-11111-1-11-11-1-1-111-222-200001-11-1-11-1100003−33−3−33−33−33−333−33−30000000000000000
χ682-2-22-22-22-22-1-2-22-2-2222-1-111-11111-1-11-11-1-1-111-222-200001-11-1-11-110000−33−333−33−33−33−3−33−330000000000000000
χ692-2-22-2-2222-222-2-2-22-222-2-2-2-2222-222-22-2-22-22-2200002-2-220000000000002-2-22-222-2000000000000000000000000
χ702-2-22-2-2222-222-2-2-22-222-2-2-2-2222-222-22-2-22-22-220000-222-2000000000000-222-22-2-22000000000000000000000000
χ712-2-22-2-2222-22-2222-22-2-2-2-2-2-2222-222-2-222-22-22-200000000000000000000000000000000000000002i−2i−2i2i00000000
χ722-2-22-2-2222-22-2222-22-2-2-2-2-2-2222-222-2-222-22-22-20000000000000000000000000000000000000000−2i2i2i−2i00000000
χ732-2-22-2-2222-2-12-2-2-22-2221111-1-1-11-1-11-111-11-11-100002-2-22−i3i3i3−i3i3−i3−i3i30000-111-11-1-11−i3i3i3−i3i3−i3−i3i30000000000000000
χ742-2-22-2-2222-2-12-2-2-22-2221111-1-1-11-1-11-111-11-11-100002-2-22i3−i3−i3i3−i3i3i3−i30000-111-11-1-11i3−i3−i3i3−i3i3i3−i30000000000000000
χ752-2-22-2-2222-2-12-2-2-22-2221111-1-1-11-1-11-111-11-11-10000-222-2−i3i3i3−i3i3−i3−i3i300001-1-11-111-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ762-2-22-2-2222-2-12-2-2-22-2221111-1-1-11-1-11-111-11-11-10000-222-2i3−i3−i3i3−i3i3i3−i300001-1-11-111-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ774444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000
χ7844444-4-44-4-4-24-44-444-4-422-2-2-222-22-22-2-222-222-20000000000000000000000000000000000000000000000000000
χ794444-44-4-44-4-2444-4-4-4-44-2-2-2-2-2-2-22222-22-22-2-2220000000000000000000000000000000000000000000000000000
χ804444-4-44-4-44-2-44-4-444-4422-2-2-2222-22-22-2-222-22-20000000000000000000000000000000000000000000000000000
χ814-4-44444-4-4-4-2-4-4444-4-44-2-222-222-2-2222222-2-2-2-20000000000000000000000000000000000000000000000000000
χ824-4-444-4-4-444-24-4-44-44-442222-2-2-2-222-2-2-2222-2-220000000000000000000000000000000000000000000000000000
χ834-4-44-44-44-44-244-444-4-4-4-2-222-22222-2-2-22-2222-2-20000000000000000000000000000000000000000000000000000
χ844-4-44-4-4444-4-2-4444-44-4-42222-2-2-22-2-222-2-22-22-220000000000000000000000000000000000000000000000000000
χ8588-8-8000000800000000008-8-8000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400000000−4i34i3-444−4i34i30000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-4000000004i3−4i3-4444i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ888-88-800000080000000000-88-8000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000-400000000−4i34i34-444i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ908-88-8000000-4000000004i3−4i34-44−4i34i30000000000000000000000000000000000000000000000000000000000000000

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