Finite Group Databasebeta

← Group #10701786

Character table — Group #10701786

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order122222222234444444466666666666121212121212121222226666666688888888242424242424242424242424242424242244444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ911111-1-11-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111-1-11-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111-1-11-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211111-1-11-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311111-1-11-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111-1-11-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111-1-11-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111-1-11-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-22-22-222-2-222-2-20000000000000000000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-22-22-2-222-2-2220000000000000000000000000000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-1110000000033−3−333−3−333−3−333−3−30000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-11100000000−3−333−3−333−3−333−3−3330000000000000000
χ252222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-10000000033−3−333−3−3−3−333−3−3330000000000000000
χ262222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-100000000−3−333−3−33333−3−333−3−30000000000000000
χ2722222-2-22-2-22-2-2-2-2222222-2-2-2-2222-2-2-2-2-2-222222-2-2222-2-2-2-2220000000000000000000000000000000000000000
χ2822222-2-22-2-22-2-2-2-2222222-2-2-2-2222-2-2-2-2-2-22222-222-2-2-22222-2-20000000000000000000000000000000000000000
χ2922222-2-22-2-2-12222-2-2-2-2-1-11111-1-1-111-1-1-1-1111122-2-2-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ3022222-2-22-2-2-12222-2-2-2-2-1-11111-1-1-111-1-1-1-1111122-2-2-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ3122222-2-22-2-2-12222-2-2-2-2-1-11111-1-1-111-1-1-1-11111-2-2221111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ3222222-2-22-2-2-12222-2-2-2-2-1-11111-1-1-111-1-1-1-11111-2-2221111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ3322222-2-22-2-2-1-2-2-2-22222-1-11111-1-1-1111111-1-1-1-12-2-22-1-11111-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3422222-2-22-2-2-1-2-2-2-22222-1-11111-1-1-1111111-1-1-1-12-2-22-1-11111-1-100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3522222-2-22-2-2-1-2-2-2-22222-1-11111-1-1-1111111-1-1-1-1-222-211-1-1-1-11100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222-2-22-2-2-1-2-2-2-22222-1-11111-1-1-1111111-1-1-1-1-222-211-1-1-1-11100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ372222-222-2-2-2222-2-22-22-22222222-2-2-2-222-2-22-22-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ382222-222-2-2-2222-2-22-22-22222222-2-2-2-222-2-22-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ392222-222-2-2-22-2-222-22-222222222-2-2-2-2-2-222-22-22000000000000000000000000000000000000000000002i−2i2i−2i0000
χ402222-222-2-2-22-2-222-22-222222222-2-2-2-2-2-222-22-2200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ412222-2-2-2-222222-2-2-22-2222-2-2-2-22-2-22222-2-2-22-220000000000000000000000000000000000000000000000002-2-22
χ422222-2-2-2-222222-2-2-22-2222-2-2-2-22-2-22222-2-2-22-22000000000000000000000000000000000000000000000000-222-2
χ432222-2-2-2-2222-2-2222-22-222-2-2-2-22-2-222-2-2222-22-2000000000000000000000000000000000000000000002-2-220000
χ442222-2-2-2-2222-2-2222-22-222-2-2-2-22-2-222-2-2222-22-200000000000000000000000000000000000000000000-222-20000
χ452-2-2222-2-22-222-22-222-2-2-2-222-2-222-22-22-22-222-2-200000000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ462-2-2222-2-22-222-22-222-2-2-2-222-2-222-22-22-22-222-2-20000000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ472-2-2222-2-22-22-22-22-2-222-2-222-2-222-22-2-22-22-2-2220000000000002-22-200002-22-22-22-2000000000000000000000000
χ482-2-2222-2-22-22-22-22-2-222-2-222-2-222-22-2-22-22-2-222000000000000-22-220000-22-22-22-22000000000000000000000000
χ492-2-2222-2-22-2-12-22-222-2-211-1-111-1-11-11-11-11-1-1110000−i3i3−i3i3−i3i3−i3i300002i−2i2i−2i3−3−333−3−33−ii−ii−ii−ii0000000000000000
χ502-2-2222-2-22-2-12-22-222-2-211-1-111-1-11-11-11-11-1-1110000−i3i3−i3i3−i3i3−i3i30000−2i2i−2i2i−333−3−333−3i−ii−ii−ii−i0000000000000000
χ512-2-2222-2-22-2-12-22-222-2-211-1-111-1-11-11-11-11-1-1110000i3−i3i3−i3i3−i3i3−i300002i−2i2i−2i−333−3−333−3−ii−ii−ii−ii0000000000000000
χ522-2-2222-2-22-2-12-22-222-2-211-1-111-1-11-11-11-11-1-1110000i3−i3i3−i3i3−i3i3−i30000−2i2i−2i2i3−3−333−3−33i−ii−ii−ii−i0000000000000000
χ532-2-2222-2-22-2-1-22-22-2-22211-1-111-1-11-111-11-111-1-10000−i3i3i3−i3−i3i3i3−i32-22-20000-11-11-11-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ542-2-2222-2-22-2-1-22-22-2-22211-1-111-1-11-111-11-111-1-10000−i3i3i3−i3−i3i3i3−i3-22-2200001-11-11-11-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ552-2-2222-2-22-2-1-22-22-2-22211-1-111-1-11-111-11-111-1-10000i3−i3−i3i3i3−i3−i3i32-22-20000-11-11-11-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ562-2-2222-2-22-2-1-22-22-2-22211-1-111-1-11-111-11-111-1-10000i3−i3−i3i3i3−i3−i3i3-22-2200001-11-11-11-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ572-2-222-22-2-2222-22-2-2-222-2-2-2-22222-2-222-22-2-2-22200000000000000002-2-22000000002-22-2-22-220000000000000000
χ582-2-222-22-2-2222-22-2-2-222-2-2-2-22222-2-222-22-2-2-2220000000000000000-222-200000000-22-222-22-20000000000000000
χ592-2-222-22-2-222-22-2222-2-2-2-2-2-22222-2-22-22-2222-2-20000000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ602-2-222-22-2-222-22-2222-2-2-2-2-2-22222-2-22-22-2222-2-2000000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ612-2-222-22-2-22-12-22-2-2-2221111-1-1-1-111-1-11-1111-1-10000−i3i3−i3i3i3−i3i3−i300002-2-22−i3i3i3−i3i3−i3−i3i3-11-111-11-10000000000000000
χ622-2-222-22-2-22-12-22-2-2-2221111-1-1-1-111-1-11-1111-1-10000−i3i3−i3i3i3−i3i3−i30000-222-2i3−i3−i3i3−i3i3i3−i31-11-1-11-110000000000000000
χ632-2-222-22-2-22-12-22-2-2-2221111-1-1-1-111-1-11-1111-1-10000i3−i3i3−i3−i3i3−i3i300002-2-22i3−i3−i3i3−i3i3i3−i3-11-111-11-10000000000000000
χ642-2-222-22-2-22-12-22-2-2-2221111-1-1-1-111-1-11-1111-1-10000i3−i3i3−i3−i3i3−i3i30000-222-2−i3i3i3−i3i3−i3−i3i31-11-1-11-110000000000000000
χ652-2-222-22-2-22-1-22-2222-2-21111-1-1-1-111-11-11-1-1-1110000−i3i3i3−i3i3−i3−i3i32i−2i−2i2i0000−ii−iii−ii−i3−3−33−333−30000000000000000
χ662-2-222-22-2-22-1-22-2222-2-21111-1-1-1-111-11-11-1-1-1110000−i3i3i3−i3i3−i3−i3i3−2i2i2i−2i0000i−ii−i−ii−ii−333−33−3−330000000000000000
χ672-2-222-22-2-22-1-22-2222-2-21111-1-1-1-111-11-11-1-1-1110000i3−i3−i3i3−i3i3i3−i32i−2i−2i2i0000−ii−iii−ii−i−333−33−3−330000000000000000
χ682-2-222-22-2-22-1-22-2222-2-21111-1-1-1-111-11-11-1-1-1110000i3−i3−i3i3−i3i3i3−i3−2i2i2i−2i0000i−ii−i−ii−ii3−3−33−333−30000000000000000
χ692-2-22-22-22-2222-2-222-2-22-2-222-2-22-22-222-2-222-2-220000000000000000000000000000000000002-22-2000000000000
χ702-2-22-22-22-2222-2-222-2-22-2-222-2-22-22-222-2-222-2-22000000000000000000000000000000000000-22-22000000000000
χ712-2-22-22-22-222-222-2-222-2-2-222-2-22-22-22-222-2-222-200000000000000000000000000000000000000002-22-200000000
χ722-2-22-22-22-222-222-2-222-2-2-222-2-22-22-22-222-2-222-20000000000000000000000000000000000000000-22-2200000000
χ732-2-22-2-2222-222-2-22-222-2-2-2-2-2222-222-22-2-22-222-20000000000000000000000000000000000002-2-22000000000000
χ742-2-22-2-2222-222-2-22-222-2-2-2-2-2222-222-22-2-22-222-2000000000000000000000000000000000000-222-2000000000000
χ752-2-22-2-2222-22-222-22-2-22-2-2-2-2222-222-2-222-22-2-2200000000000000000000000000000000000000002-2-2200000000
χ762-2-22-2-2222-22-222-22-2-22-2-2-2-2222-222-2-222-22-2-220000000000000000000000000000000000000000-222-200000000
χ774444-444-4-4-4-244-4-44-44-4-2-2-2-2-2-2-22222-2-222-22-220000000000000000000000000000000000000000000000000000
χ784444-444-4-4-4-2-4-444-44-44-2-2-2-2-2-2-2222222-2-22-22-20000000000000000000000000000000000000000000000000000
χ794444-4-4-4-444-244-4-4-44-44-2-22222-222-2-2-2-2222-22-20000000000000000000000000000000000000000000000000000
χ804444-4-4-4-444-2-4-4444-44-4-2-22222-222-2-222-2-2-22-220000000000000000000000000000000000000000000000000000
χ814-4-44-44-44-44-24-4-444-4-4422-2-222-22-22-2-222-2-222-20000000000000000000000000000000000000000000000000000
χ824-4-44-44-44-44-2-444-4-444-422-2-222-22-22-22-2-222-2-220000000000000000000000000000000000000000000000000000
χ834-4-44-4-4444-4-24-4-44-444-42222-2-2-22-2-22-222-22-2-220000000000000000000000000000000000000000000000000000
χ844-4-44-4-4444-4-2-444-44-4-442222-2-2-22-2-222-2-22-222-20000000000000000000000000000000000000000000000000000
χ8588-8-80000008000000008-80000-80000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400000000-44−4i34i3−4i34i340000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-400000000-444i3−4i34i3−4i340000000000000000000000000000000000000000000000000000000000000000
χ888-88-8000000800000000-880000-80000000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000-4000000004-4−4i34i34i3−4i340000000000000000000000000000000000000000000000000000000000000000
χ908-88-8000000-4000000004-44i3−4i3−4i34i340000000000000000000000000000000000000000000000000000000000000000

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