Finite Group Databasebeta

← Group #10702892

Character table — Group #10702892

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222222223444444446666666666612121212121212124444888888881212121212121212242424242424242424242424242424242244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
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
χ911111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1ii−i−iii−i−i
χ1011111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−i−iii−i−iii
χ1111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−i−iii−i−iii
χ1211111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111ii−i−iii−i−i
χ1311111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111ii−i−i−i−iii
χ1411111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1−i−iiiii−i−i
χ1511111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111−i−iiiii−i−i
χ1611111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1ii−i−i−i−iii
χ172222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ25222222-2-2-2-22222-22-2-2-22222222-2-2-2-2222-2-2-22-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ26222222-2-2-2-22222-22-2-2-22222222-2-2-2-2222-2-2-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ27222222-2-2-2-22-2-2-22-22222222222-2-2-2-2-2-2-2222-220000000000000000000000000000000000000000000000002-2-22
χ28222222-2-2-2-22-2-2-22-22222222222-2-2-2-2-2-2-2222-22000000000000000000000000000000000000000000000000-222-2
χ292222-2-222-2-2222-22-2-22-22-2-2-2-22222-2-222-222-2-2-2000000002i−2i2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ302222-2-222-2-2222-22-2-22-22-2-2-2-22222-2-222-222-2-2-200000000−2i2i−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ312222-2-222-2-22-2-22-222-222-2-2-2-22222-2-2-2-22-2-2222000000002-2-22000000000000000022-2-2-2-2220000000000000000
χ322222-2-222-2-22-2-22-222-222-2-2-2-22222-2-2-2-22-2-222200000000-222-20000000000000000-2-22222-2-20000000000000000
χ332222-2-222-2-2-122-22-2-22-2-11111-1-1-1-111-1-11-1-1111000000002i−2i2i−2i−i3−i3i3i3−i3−i3i3i333−3−333−3−3−i−iii−i−iii0000000000000000
χ342222-2-222-2-2-122-22-2-22-2-11111-1-1-1-111-1-11-1-1111000000002i−2i2i−2ii3i3−i3−i3i3i3−i3−i3−3−333−3−333−i−iii−i−iii0000000000000000
χ352222-2-222-2-2-122-22-2-22-2-11111-1-1-1-111-1-11-1-111100000000−2i2i−2i2i−i3−i3i3i3−i3−i3i3i3−3−333−3−333ii−i−iii−i−i0000000000000000
χ362222-2-222-2-2-122-22-2-22-2-11111-1-1-1-111-1-11-1-111100000000−2i2i−2i2ii3i3−i3−i3i3i3−i3−i333−3−333−3−3ii−i−iii−i−i0000000000000000
χ372222-2-222-2-2-1-2-22-222-22-11111-1-1-1-11111-111-1-1-1000000002-2-22−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000000000
χ382222-2-222-2-2-1-2-22-222-22-11111-1-1-1-11111-111-1-1-1000000002-2-22i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000000000
χ392222-2-222-2-2-1-2-22-222-22-11111-1-1-1-11111-111-1-1-100000000-222-2−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000000000
χ402222-2-222-2-2-1-2-22-222-22-11111-1-1-1-11111-111-1-1-100000000-222-2i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000000000
χ412222-2-2-2-222222-2-2-22-222-2-2-2-222-2-22222-2-2-22-220000000000000000000000000000000000002-2-22000000000000
χ422222-2-2-2-222222-2-2-22-222-2-2-2-222-2-22222-2-2-22-22000000000000000000000000000000000000-222-2000000000000
χ432222-2-2-2-2222-2-2222-22-22-2-2-2-222-2-222-2-2222-22-200000000000000000000000000000000000022-2-2000000000000
χ442222-2-2-2-2222-2-2222-22-22-2-2-2-222-2-222-2-2222-22-2000000000000000000000000000000000000-2-222000000000000
χ452-2-222-22-22-222-22-2-222-2-222-2-22-22-22-22-222-2-2-222i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ462-2-222-22-22-222-22-2-222-2-222-2-22-22-22-22-222-2-2-22−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ472-2-222-22-22-22-22-222-2-22-222-2-22-22-22-2-22-2-2222-22i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ482-2-222-22-22-22-22-222-2-22-222-2-22-22-22-2-22-2-2222-2−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ492-2-222-22-22-2-12-22-2-222-21-1-111-11-11-11-11-1-1111-12i−2i2i−2i00000000−ii−ii−ii−ii3−33−33−33−3−i3i3−i3i3−i3i3−i3i30000000000000000
χ502-2-222-22-22-2-12-22-2-222-21-1-111-11-11-11-11-1-1111-12i−2i2i−2i00000000−ii−ii−ii−ii−33−33−33−33i3−i3i3−i3i3−i3i3−i30000000000000000
χ512-2-222-22-22-2-12-22-2-222-21-1-111-11-11-11-11-1-1111-1−2i2i−2i2i00000000i−ii−ii−ii−i3−33−33−33−3i3−i3i3−i3i3−i3i3−i30000000000000000
χ522-2-222-22-22-2-12-22-2-222-21-1-111-11-11-11-11-1-1111-1−2i2i−2i2i00000000i−ii−ii−ii−i−33−33−33−33−i3i3−i3i3−i3i3−i3i30000000000000000
χ532-2-222-22-22-2-1-22-222-2-221-1-111-11-11-111-111-1-1-112i−2i−2i2i00000000−ii−iii−ii−i−i3i3−i3i3i3−i3i3−i3−33−333−33−30000000000000000
χ542-2-222-22-22-2-1-22-222-2-221-1-111-11-11-111-111-1-1-112i−2i−2i2i00000000−ii−iii−ii−ii3−i3i3−i3−i3i3−i3i33−33−3−33−330000000000000000
χ552-2-222-22-22-2-1-22-222-2-221-1-111-11-11-111-111-1-1-11−2i2i2i−2i00000000i−ii−i−ii−ii−i3i3−i3i3i3−i3i3−i33−33−3−33−330000000000000000
χ562-2-222-22-22-2-1-22-222-2-221-1-111-11-11-111-111-1-1-11−2i2i2i−2i00000000i−ii−i−ii−iii3−i3i3−i3−i3i3−i3i3−33−333−33−30000000000000000
χ572-2-222-2-22-2222-222-2-2-22-222-2-22-2-22-222-22-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ582-2-222-2-22-2222-222-2-2-22-222-2-22-2-22-222-22-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ592-2-222-2-22-222-22-2-2222-2-222-2-22-2-22-22-22-22-2-222000000000000000000000000000000000000000000002-2-220000
χ602-2-222-2-22-222-22-2-2222-2-222-2-22-2-22-22-22-22-2-22200000000000000000000000000000000000000000000-222-20000
χ612-2-22-222-2-2222-2-2-22-222-2-2-2222-22-2-222-2-22-222-200002-22-20000000000002-2-222-2-22000000000000000000000000
χ622-2-22-222-2-2222-2-2-22-222-2-2-2222-22-2-222-2-22-222-20000-22-22000000000000-222-2-222-2000000000000000000000000
χ632-2-22-222-2-222-2222-22-2-2-2-2-2222-22-2-22-222-22-2-2200002i−2i−2i2i0000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ642-2-22-222-2-222-2222-22-2-2-2-2-2222-22-2-22-222-22-2-220000−2i2i2i−2i000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ652-2-22-222-2-22-12-2-2-22-222111-1-1-11-111-1-111-11-1-1100002-22-200003−3−333−3−33-111-1-111-1−333−3−333−30000000000000000
χ662-2-22-222-2-22-12-2-2-22-222111-1-1-11-111-1-111-11-1-1100002-22-20000−333−3−333−3-111-1-111-13−3−333−3−330000000000000000
χ672-2-22-222-2-22-12-2-2-22-222111-1-1-11-111-1-111-11-1-110000-22-2200003−3−333−3−331-1-111-1-113−3−333−3−330000000000000000
χ682-2-22-222-2-22-12-2-2-22-222111-1-1-11-111-1-111-11-1-110000-22-220000−333−3−333−31-1-111-1-11−333−3−333−30000000000000000
χ692-2-22-222-2-22-1-2222-22-2-2111-1-1-11-111-11-1-11-111-100002i−2i−2i2i00003−3−33−333−3−iii−ii−i−ii−i3i3i3−i3i3−i3−i3i30000000000000000
χ702-2-22-222-2-22-1-2222-22-2-2111-1-1-11-111-11-1-11-111-100002i−2i−2i2i0000−333−33−3−33−iii−ii−i−iii3−i3−i3i3−i3i3i3−i30000000000000000
χ712-2-22-222-2-22-1-2222-22-2-2111-1-1-11-111-11-1-11-111-10000−2i2i2i−2i00003−3−33−333−3i−i−ii−iii−ii3−i3−i3i3−i3i3i3−i30000000000000000
χ722-2-22-222-2-22-1-2222-22-2-2111-1-1-11-111-11-1-11-111-10000−2i2i2i−2i0000−333−33−3−33i−i−ii−iii−i−i3i3i3−i3i3−i3−i3i30000000000000000
χ732-2-22-22-222-222-2-2222-2-2-2-2-2222-2-222-22-2-2-22-22200000000000000000000000000000000000000002i−2i2i−2i00000000
χ742-2-22-22-222-222-2-2222-2-2-2-2-2222-2-222-22-2-2-22-2220000000000000000000000000000000000000000−2i2i−2i2i00000000
χ752-2-22-22-222-22-222-2-2-222-2-2-2222-2-222-2-2222-22-2-200000000000000000000000000000000000000002i−2i−2i2i00000000
χ762-2-22-22-222-22-222-2-2-222-2-2-2222-2-222-2-2222-22-2-20000000000000000000000000000000000000000−2i2i2i−2i00000000
χ77444444-4-4-4-4-2444-44-4-4-4-2-2-2-2-2-2-22222-2-2-2222-220000000000000000000000000000000000000000000000000000
χ78444444-4-4-4-4-2-4-4-44-4444-2-2-2-2-2-2-22222222-2-2-22-20000000000000000000000000000000000000000000000000000
χ794444-4-4-4-444-244-4-4-44-44-22222-2-222-2-2-2-2222-22-20000000000000000000000000000000000000000000000000000
χ804444-4-4-4-444-2-4-4444-44-4-22222-2-222-2-222-2-2-22-220000000000000000000000000000000000000000000000000000
χ814-4-444-4-44-44-24-444-4-4-442-2-222-222-22-2-22-22-2-2220000000000000000000000000000000000000000000000000000
χ824-4-444-4-44-44-2-44-4-4444-42-2-222-222-22-22-22-222-2-20000000000000000000000000000000000000000000000000000
χ834-4-44-44-444-4-24-4-4444-4-4222-2-2-222-2-22-2222-22-2-20000000000000000000000000000000000000000000000000000
χ844-4-44-44-444-4-2-444-4-4-444222-2-2-222-2-222-2-2-22-2220000000000000000000000000000000000000000000000000000
χ8588-8-800000080000000080000-8-80000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400000000-4−4i34i3−4i34i3440000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-400000000-44i3−4i34i3−4i3440000000000000000000000000000000000000000000000000000000000000000
χ888-88-8000000800000000-80000-880000000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000-4000000004−4i34i34i3−4i34-40000000000000000000000000000000000000000000000000000000000000000
χ908-88-8000000-40000000044i3−4i3−4i34i34-40000000000000000000000000000000000000000000000000000000000000000

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