Finite Group Databasebeta

← Group #10840245

Character table — Group #10840245

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order122222223444466666664444444412121212121212121212121244444488881212121212121212121212121212121224242424242424242244244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111
χ6111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1
χ7111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1
χ8111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-111
χ911111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-111111-1-11-1
χ1011111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-111-11
χ1111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1111-1-111-11
χ1211111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111-1-1-111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-111-1-11-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111-1-111-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-111-1-1111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111-1-111-1-1-1111-1
χ17222222222-2-2-2-2222222222-2-200002222-2-2-2-2-2-2-2-2000000000000000000000000000000000022-2-220000-2000000
χ18222222222-2-2-2-2222222222-2-200002222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-222-200002000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-22222-2-200000000000000000000000000000000002222-20000-2000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-22222-2-20000000000000000000000000000000000-2-2-2-2200002000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-11111-1-1-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-11111-1-1-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-11111-1-12222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-11111-1-122-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ2922-22-2-22-222-2-22-2-22-2-2222-22-22i2i−2i−2i22-2-22222-2-2-2-22i−2i000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ3022-22-2-22-222-2-22-2-22-2-2222-22-2−2i−2i2i2i22-2-22222-2-2-2-2−2i2i00000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ3122-22-2-22-222-2-22-2-22-2-222-22-222i2i−2i−2i-2-22222-2-222-2-2−2i2i000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ3222-22-2-22-222-2-22-2-22-2-222-22-22−2i−2i2i2i-2-22222-2-222-2-22i−2i00000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ3322-22-2-22-22-222-2-2-22-2-2222-2-22000022-2-2-2-2-2-222220000000000000000000000000000000000000002i−2i2i−2i0000000
χ3422-22-2-22-22-222-2-2-22-2-2222-2-22000022-2-2-2-2-2-22222000000000000000000000000000000000000000−2i2i−2i2i0000000
χ3522-22-2-22-22-222-2-2-22-2-222-222-20000-2-222-2-222-2-2220000000000000000000000000000000000000002i−2i−2i2i0000000
χ3622-22-2-22-22-222-2-2-22-2-222-222-20000-2-222-2-222-2-222000000000000000000000000000000000000000−2i2i2i−2i0000000
χ3722-22-2-22-2-12-2-2211-111-1-12-22-22i2i−2i−2i-1-111-1-1-1-111112i−2i00000000−i−iii−i−iii−i3−i3i3i3−i3−i3i3i333−3−333−3−30000000000000000
χ3822-22-2-22-2-12-2-2211-111-1-12-22-22i2i−2i−2i-1-111-1-1-1-111112i−2i00000000−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3−3−333−3−3330000000000000000
χ3922-22-2-22-2-12-2-2211-111-1-12-22-2−2i−2i2i2i-1-111-1-1-1-11111−2i2i00000000ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i3−3−333−3−3330000000000000000
χ4022-22-2-22-2-12-2-2211-111-1-12-22-2−2i−2i2i2i-1-111-1-1-1-11111−2i2i00000000ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i333−3−333−3−30000000000000000
χ4122-22-2-22-2-12-2-2211-111-1-1-22-222i2i−2i−2i11-1-1-1-111-1-111−2i2i00000000−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i333−3−3−3−3330000000000000000
χ4222-22-2-22-2-12-2-2211-111-1-1-22-222i2i−2i−2i11-1-1-1-111-1-111−2i2i00000000−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i3−3−33333−3−30000000000000000
χ4322-22-2-22-2-12-2-2211-111-1-1-22-22−2i−2i2i2i11-1-1-1-111-1-1112i−2i00000000ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i3−3−33333−3−30000000000000000
χ4422-22-2-22-2-12-2-2211-111-1-1-22-22−2i−2i2i2i11-1-1-1-111-1-1112i−2i00000000ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i333−3−3−3−3330000000000000000
χ452-22-2-2-222222-2-22-2-22-22-200002i−2i2i−2i00002-200002-200002-2002i−2i2i−2i2i−2i000000002-22-200002i−2i2i−2i0000000000000000
χ462-22-2-2-222222-2-22-2-22-22-200002i−2i2i−2i00002-200002-20000-2200−2i2i2i−2i2i−2i00000000-22-220000−2i2i−2i2i0000000000000000
χ472-22-2-2-222222-2-22-2-22-22-20000−2i2i−2i2i00002-200002-200002-200−2i2i−2i2i−2i2i000000002-22-20000−2i2i−2i2i0000000000000000
χ482-22-2-2-222222-2-22-2-22-22-20000−2i2i−2i2i00002-200002-20000-22002i−2i−2i2i−2i2i00000000-22-2200002i−2i2i−2i0000000000000000
χ492-22-2-2-222-122-2-2-111-11-1100002i−2i2i−2i3−33−3-113−33−3-1100002-2002i−2i−ii−ii−i3i3−i3i33−33−3-11-11−i3i3−i3i3−ii−ii0000000000000000
χ502-22-2-2-222-122-2-2-111-11-1100002i−2i2i−2i3−33−3-113−33−3-110000-2200−2i2i−ii−ii−i3i3−i3i3−33−331-11-1i3−i3i3−i3i−ii−i0000000000000000
χ512-22-2-2-222-122-2-2-111-11-1100002i−2i2i−2i−33−33-11−33−33-1100002-2002i−2i−ii−iii3−i3i3−i3−33−33-11-11i3−i3i3−i3−ii−ii0000000000000000
χ522-22-2-2-222-122-2-2-111-11-1100002i−2i2i−2i−33−33-11−33−33-110000-2200−2i2i−ii−iii3−i3i3−i33−33−31-11-1−i3i3−i3i3i−ii−i0000000000000000
χ532-22-2-2-222-122-2-2-111-11-110000−2i2i−2i2i3−33−3-113−33−3-1100002-200−2i2ii−ii−ii3−i3i3−i33−33−3-11-11i3−i3i3−i3i−ii−i0000000000000000
χ542-22-2-2-222-122-2-2-111-11-110000−2i2i−2i2i3−33−3-113−33−3-110000-22002i−2ii−ii−ii3−i3i3−i3−33−331-11-1−i3i3−i3i3−ii−ii0000000000000000
χ552-22-2-2-222-122-2-2-111-11-110000−2i2i−2i2i−33−33-11−33−33-1100002-200−2i2ii−ii−i−i3i3−i3i3−33−33-11-11−i3i3−i3i3i−ii−i0000000000000000
χ562-22-2-2-222-122-2-2-111-11-110000−2i2i−2i2i−33−33-11−33−33-110000-22002i−2ii−ii−i−i3i3−i3i33−33−31-11-1i3−i3i3−i3−ii−ii0000000000000000
χ572-2-2-2222-222-22-2-22-2-222-200002-2-2200002-20000-22002i−2i002i−2i002-2-2200002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ582-2-2-2222-222-22-2-22-2-222-200002-2-2200002-20000-2200−2i2i00−2i2i002-2-220000−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ592-2-2-2222-222-22-2-22-2-222-20000-222-200002-20000-22002i−2i00−2i2i00-222-200002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ602-2-2-2222-222-22-2-22-2-222-20000-222-200002-20000-2200−2i2i002i−2i00-222-20000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ612-2-2-2222-2-12-22-21-111-1-1100002-2-223−3−33-113−3−331-1002i−2i002i−2i00-111-1−333−3−iii−i−i3i3i3−i3i−i−ii−i3i3i3−i30000000000000000
χ622-2-2-2222-2-12-22-21-111-1-1100002-2-223−3−33-113−3−331-100−2i2i00−2i2i00-111-1−333−3i−i−iii3−i3−i3i3−iii−ii3−i3−i3i30000000000000000
χ632-2-2-2222-2-12-22-21-111-1-1100002-2-22−333−3-11−333−31-1002i−2i002i−2i00-111-13−3−33−iii−ii3−i3−i3i3i−i−iii3−i3−i3i30000000000000000
χ642-2-2-2222-2-12-22-21-111-1-1100002-2-22−333−3-11−333−31-100−2i2i00−2i2i00-111-13−3−33i−i−ii−i3i3i3−i3−iii−i−i3i3i3−i30000000000000000
χ652-2-2-2222-2-12-22-21-111-1-110000-222-23−3−33-113−3−331-1002i−2i00−2i2i001-1-113−3−33−iii−i−i3i3i3−i3−iii−ii3−i3−i3i30000000000000000
χ662-2-2-2222-2-12-22-21-111-1-110000-222-23−3−33-113−3−331-100−2i2i002i−2i001-1-113−3−33i−i−iii3−i3−i3i3i−i−ii−i3i3i3−i30000000000000000
χ672-2-2-2222-2-12-22-21-111-1-110000-222-2−333−3-11−333−31-1002i−2i00−2i2i001-1-11−333−3−iii−ii3−i3−i3i3−iii−i−i3i3i3−i30000000000000000
χ682-2-2-2222-2-12-22-21-111-1-110000-222-2−333−3-11−333−31-100−2i2i002i−2i001-1-11−333−3i−i−ii−i3i3i3−i3i−i−iii3−i3−i3i30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ71444-44-4-4-440000-4444-4-4-40000000000000000000000000000000000000000000000000000004-400000000000000
χ72444-44-4-4-440000-4444-4-4-4000000000000000000000000000000000000000000000000000000-4400000000000000
χ7344-44-4-44-4-2-444-422-222-2-24-4-440000-2-2222222-2-2-2-200000000000000000000000000000000000000000000000000
χ7444-44-4-44-4-2-444-422-222-2-2-444-4000022-2-222-2-222-2-200000000000000000000000000000000000000000000000000
χ7544-4-4-44-44400004-44-44-4-4000000000000000000000000000000000000000000000000000000004i−4i000000000000
χ7644-4-4-44-44400004-44-44-4-400000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ774-444-44-4-440000-4-4-444-44000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ784-444-44-4-440000-4-4-444-440000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ794-44-4-4-4444-4-4444-4-44-44-4000000000000-440000-4400000000000000000000000000000000000000000000000000
χ804-44-4-4-444-2-4-444-222-22-220000000023−2323−232-2−2323−23232-200000000000000000000000000000000000000000000000000
χ814-44-4-4-444-2-4-444-222-22-2200000000−2323−23232-223−2323−232-200000000000000000000000000000000000000000000000000
χ824-4-444-4-444000044-4-4-4-440000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ834-4-444-4-444000044-4-4-4-4400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ844-4-4-4444-44-44-44-44-4-444-4000000000000-4400004-400000000000000000000000000000000000000000000000000
χ854-4-4-4444-4-2-44-442-222-2-220000000023−23−23232-2−232323−23-2200000000000000000000000000000000000000000000000000
χ864-4-4-4444-4-2-44-442-222-2-2200000000−232323−232-223−23−2323-2200000000000000000000000000000000000000000000000000
χ87888-88-8-8-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-88-88-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-88-8-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-8-88-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000

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