Finite Group Databasebeta

← Group #10702209

Character table — Group #10702209

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122222222222344444444666666666661212121212121212222244446666666688881212121212121212242424242424242488888888444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ91-1-1-1111-111-1-11111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−iii−i−iii−i−i
χ101-1-1-1111-111-1-11111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii−i−iii
χ111-1-1-1111-111-1-11111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111iiii−i−i−i−iii−i−i−i−iii−i−iii
χ121-1-1-1111-111-1-11111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−iiiii−i−iii−i−i
χ131-1-1-1111-111-1-11111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii−i−iiiii−i−i
χ141-1-1-1111-111-1-11111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−iii−i−i−i−iii
χ151-1-1-1111-111-1-11111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−iiiii−i−i−i−iii
χ161-1-1-1111-111-1-11111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiii−i−i−i−iiiii−i−i
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2111111111111111100000000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211111111-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111222211111111-1-1-1-1-1-1-1-100000000000000000000
χ2322222222-2-2-2-2222-22-2-2-222222222-2-2-2-222-222-2-2-200000000000000000000000000000000000022-2-222-2-2000000000000
χ2422222222-2-2-2-2222-22-2-2-222222222-2-2-2-222-222-2-2-2000000000000000000000000000000000000-2-222-2-222000000000000
χ2522222222-2-2-2-22-2-22-2222-22222222-2-2-2-2-2-22-2-222200002-22-200000000000022-2-222-2-20000000000000000000000000000
χ2622222222-2-2-2-22-2-22-2222-22222222-2-2-2-2-2-22-2-22220000-22-22000000000000-2-222-2-2220000000000000000000000000000
χ2722222222-2-2-2-2-1-2-22-2222-2-1-1-1-1-1-1-1111111-111-1-1-100002-22-2−i3−i3i3i3−i3−i3i3i30000-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2822222222-2-2-2-2-1-2-22-2222-2-1-1-1-1-1-1-1111111-111-1-1-100002-22-2i3i3−i3−i3i3i3−i3−i30000-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000000000
χ2922222222-2-2-2-2-1-2-22-2222-2-1-1-1-1-1-1-1111111-111-1-1-10000-22-22−i3−i3i3i3−i3−i3i3i3000011-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000000000
χ3022222222-2-2-2-2-1-2-22-2222-2-1-1-1-1-1-1-1111111-111-1-1-10000-22-22i3i3−i3−i3i3i3−i3−i3000011-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000000000
χ31222-22-2-2-22-22-222-2222-2-2-222-2-22-2-22-22-22-222-22-2-22-22-200002-22-22-22-20000000000000000000000000000000000000000
χ32222-22-2-2-22-22-222-2222-2-2-222-2-22-2-22-22-22-222-22-2-2-22-220000-22-22-22-220000000000000000000000000000000000000000
χ33222-22-2-2-22-22-22-22-2-2-222222-2-22-2-22-22-2-22-2-22-2220000000000000000000000000000000000000000000000002-22-20000
χ34222-22-2-2-22-22-22-22-2-2-222222-2-22-2-22-22-2-22-2-22-222000000000000000000000000000000000000000000000000-22-220000
χ35222-22-2-2-22-22-2-12-2222-2-2-2-1-111-111-11-11-11-1-11-1112-22-20000-11-11-11-1100003−33−33−33−33−33−33−33−300000000000000000000
χ36222-22-2-2-22-22-2-12-2222-2-2-2-1-111-111-11-11-11-1-11-1112-22-20000-11-11-11-110000−33−33−33−33−33−33−33−3300000000000000000000
χ37222-22-2-2-22-22-2-12-2222-2-2-2-1-111-111-11-11-11-1-11-111-22-2200001-11-11-11-100003−33−33−33−3−33−33−33−3300000000000000000000
χ38222-22-2-2-22-22-2-12-2222-2-2-2-1-111-111-11-11-11-1-11-111-22-2200001-11-11-11-10000−33−33−33−333−33−33−33−300000000000000000000
χ39222-22-2-2-2-22-2222-2-22-222-222-2-22-2-2-22-222-2-22-2-222000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ40222-22-2-2-2-22-2222-2-22-222-222-2-22-2-2-22-222-2-22-2-22200000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ41222-22-2-2-2-22-222-222-22-2-2222-2-22-2-2-22-22-222-222-2-200000000000000002i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ42222-22-2-2-2-22-222-222-22-2-2222-2-22-2-2-22-22-222-222-2-20000000000000000−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ43222-22-2-2-2-22-22-1-222-22-2-22-1-111-1111-11-11-1-11-1-11100000000−i3i3i3−i3−i3i3i3−i32i−2i2i−2i3−3−333−3−33−iii−i−iii−i00000000000000000000
χ44222-22-2-2-2-22-22-1-222-22-2-22-1-111-1111-11-11-1-11-1-11100000000−i3i3i3−i3−i3i3i3−i3−2i2i−2i2i−333−3−333−3i−i−iii−i−ii00000000000000000000
χ45222-22-2-2-2-22-22-1-222-22-2-22-1-111-1111-11-11-1-11-1-11100000000i3−i3−i3i3i3−i3−i3i32i−2i2i−2i−333−3−333−3−iii−i−iii−i00000000000000000000
χ46222-22-2-2-2-22-22-1-222-22-2-22-1-111-1111-11-11-1-11-1-11100000000i3−i3−i3i3i3−i3−i3i3−2i2i−2i2i3−3−333−3−33i−i−iii−i−ii00000000000000000000
χ472-2-222-2-222-2-2222-22-2-2-222-2-2222-2-22-2-222-22-22-22-22-2-2200002-22-2-22-220000000000000000000000000000000000000000
χ482-2-222-2-222-2-2222-22-2-2-222-2-2222-2-22-2-222-22-22-22-2-222-20000-22-222-22-20000000000000000000000000000000000000000
χ492-2-222-2-222-2-222-22-2222-2-2-2-2222-2-22-2-22-22-22-22-220000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ502-2-222-2-222-2-222-22-2222-2-2-2-2222-2-22-2-22-22-22-22-22000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ512-2-222-2-222-2-22-12-22-2-2-22211-1-1-111-111-1-11-11-11-112-2-220000-11-111-11-100003−33−3−33−333−33−3−33−3300000000000000000000
χ522-2-222-2-222-2-22-12-22-2-2-22211-1-1-111-111-1-11-11-11-112-2-220000-11-111-11-10000−33−333−33−3−33−333−33−300000000000000000000
χ532-2-222-2-222-2-22-12-22-2-2-22211-1-1-111-111-1-11-11-11-11-222-200001-11-1-11-1100003−33−3−33−33−33−333−33−300000000000000000000
χ542-2-222-2-222-2-22-12-22-2-2-22211-1-1-111-111-1-11-11-11-11-222-200001-11-1-11-110000−33−333−33−33−33−3−33−3300000000000000000000
χ552-2-222-2-22-222-222-2-2-222-22-2-2222-2-2-222-22-2-2-222-22000000000000000000000000000000000000000000002-2-2200000000
χ562-2-222-2-22-222-222-2-2-222-22-2-2222-2-2-222-22-2-2-222-2200000000000000000000000000000000000000000000-222-200000000
χ572-2-222-2-22-222-22-2222-2-22-2-2-2222-2-2-222-2-2222-2-22-200000000000000002i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ582-2-222-2-22-222-22-2222-2-22-2-2-2222-2-2-222-2-2222-2-22-20000000000000000−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ592-2-222-2-22-222-2-1-2222-2-22-211-1-1-1111-1-111-1-1-111-1100000000−i3i3i3−i3i3−i3−i3i32i−2i−2i2i3−3−33−333−3−iii−ii−i−ii00000000000000000000
χ602-2-222-2-22-222-2-1-2222-2-22-211-1-1-1111-1-111-1-1-111-1100000000−i3i3i3−i3i3−i3−i3i3−2i2i2i−2i−333−33−3−33i−i−ii−iii−i00000000000000000000
χ612-2-222-2-22-222-2-1-2222-2-22-211-1-1-1111-1-111-1-1-111-1100000000i3−i3−i3i3−i3i3i3−i32i−2i−2i2i−333−33−3−33−iii−ii−i−ii00000000000000000000
χ622-2-222-2-22-222-2-1-2222-2-22-211-1-1-1111-1-111-1-1-111-1100000000i3−i3−i3i3−i3i3i3−i3−2i2i2i−2i3−3−33−333−3i−i−ii−iii−i00000000000000000000
χ632-2-2-2222-222-2-22-2-2-222-222-2-2-2-222222-2-2-2-2-22222-200000000000000000000000000000000000000000000000000002-2-22
χ642-2-2-2222-222-2-22-2-2-222-222-2-2-2-222222-2-2-2-2-22222-20000000000000000000000000000000000000000000000000000-222-2
χ652-2-2-2222-222-2-2-1222-2-22-2-21111-1-1-1-1-111-1-1-11111-122-2-222-2-2-1-1-1-1111122-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
χ662-2-2-2222-222-2-2-1222-2-22-2-21111-1-1-1-1-111-1-1-11111-122-2-2-2-222-1-1-1-11111-2-2221111-1-1-1-11111-1-1-1-100000000000000000000
χ672-2-2-2222-222-2-2-1222-2-22-2-21111-1-1-1-1-111-1-1-11111-1-2-22222-2-21111-1-1-1-1-2-222-1-1-1-111111111-1-1-1-100000000000000000000
χ682-2-2-2222-222-2-2-1222-2-22-2-21111-1-1-1-1-111-1-1-11111-1-2-222-2-2221111-1-1-1-122-2-21111-1-1-1-1-1-1-1-1111100000000000000000000
χ692-2-2-2222-2-2-222222-2-22-22-2-2-2-2-2222-2-22222-2-2-222-20000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ702-2-2-2222-2-2-222222-2-22-22-2-2-2-2-2222-2-22222-2-2-222-2000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ712-2-2-2222-2-2-2222-2-222-22-22-2-2-2-2222-2-222-2-2222-2-2200002-2-2200000000000022-2-2-2-2220000000000000000000000000000
χ722-2-2-2222-2-2-2222-2-222-22-22-2-2-2-2222-2-222-2-2222-2-220000-222-2000000000000-2-22222-2-20000000000000000000000000000
χ732-2-2-2222-2-2-222-1-2-222-22-221111-1-1-111-1-111-1-1-111-100002-2-22−i3−i3i3i3i3i3−i3−i30000-1-11111-1-1−i3−i3i3i3i3i3−i3−i300000000000000000000
χ742-2-2-2222-2-2-222-1-2-222-22-221111-1-1-111-1-111-1-1-111-100002-2-22i3i3−i3−i3−i3−i3i3i30000-1-11111-1-1i3i3−i3−i3−i3−i3i3i300000000000000000000
χ752-2-2-2222-2-2-222-1-2-222-22-221111-1-1-111-1-111-1-1-111-10000-222-2−i3−i3i3i3i3i3−i3−i3000011-1-1-1-111i3i3−i3−i3−i3−i3i3i300000000000000000000
χ762-2-2-2222-2-2-222-1-2-222-22-221111-1-1-111-1-111-1-1-111-10000-222-2i3i3−i3−i3−i3−i3i3i3000011-1-1-1-111−i3−i3i3i3i3i3−i3−i300000000000000000000
χ77444444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-4-244-44-4-4-44-2-2-2-2-2-2-22222-2-22-2-222200000000000000000000000000000000000000000000000000000000
χ79444-44-4-4-44-44-4-2-44-4-4-4444-2-222-222-22-222-222-22-2-200000000000000000000000000000000000000000000000000000000
χ80444-44-4-4-4-44-44-24-4-44-444-4-2-222-2222-22-2-222-222-2-200000000000000000000000000000000000000000000000000000000
χ8144-44-44-4-400004000000004-44-4-44-400000000000000000000000000000000000000000000000000−2i22i200−2i22i2000000000000
χ8244-44-44-4-400004000000004-44-4-44-4000000000000000000000000000000000000000000000000002i2−2i2002i2−2i2000000000000
χ8344-4-4-4-44400004000000004-4-44-4-4400000000000000000000000000000000000000000000000022−220022−2200000000000000
χ8444-4-4-4-44400004000000004-4-44-4-44000000000000000000000000000000000000000000000000−222200−222200000000000000
χ854-444-4-44-40000400000000-444-4-4-44000000000000000000000000000000000000000000000000−2i22i2002i2−2i200000000000000
χ864-444-4-44-40000400000000-444-4-4-440000000000000000000000000000000000000000000000002i2−2i200−2i22i200000000000000
χ874-44-4-44-440000400000000-44-44-44-40000000000000000000000000000000000000000000000000022−2200−2222000000000000
χ884-44-4-44-440000400000000-44-44-44-400000000000000000000000000000000000000000000000000−22220022−22000000000000
χ894-4-444-4-444-4-44-2-44-4444-4-422-2-2-222-222-22-22-22-22-200000000000000000000000000000000000000000000000000000000
χ904-4-444-4-44-444-4-24-4-4-444-4422-2-2-2222-2-22-2222-2-22-200000000000000000000000000000000000000000000000000000000
χ914-4-4-4444-444-4-4-2-4-4-444-4442222-2-2-2-2-222222-2-2-2-2200000000000000000000000000000000000000000000000000000000
χ924-4-4-4444-4-4-444-244-4-44-44-42222-2-2-222-2-2-2-2222-2-2200000000000000000000000000000000000000000000000000000000
χ9388-88-88-8-80000-400000000-44-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-8-8880000-400000000-444-444-400000000000000000000000000000000000000000000000000000000000000000000
χ958-888-8-88-80000-4000000004-4-4444-400000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-88-880000-4000000004-44-44-4400000000000000000000000000000000000000000000000000000000000000000000

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