Finite Group Databasebeta

← Group #10844911

Character table — Group #10844911

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212121212122424242448484848
order12222222344446666666444488881212121212121212121212122244444466668812121212121212121212121224242424242424244444888844882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ6111111111111111111111111-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ7111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ8111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ911111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ1111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-11-1-11
χ1211111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-11
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-11-11
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11-11-1
χ17222222222-2-2-2-2222222222-2-20000-2-22222-2-2-2-2-2-2000000000000000000000000000000000022-2-20000-22000000
χ18222222222-2-2-2-2222222222-2-20000-2-22222-2-2-2-2-2-20000000000000000000000000000000000-2-22200002-2000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-22222-2-2000000000000000000000000000000000022-2-200002-2000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-22222-2-20000000000000000000000000000000000-2-2220000-22000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111122111111111111-1-1-1-1-1-1-1-10000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-2-211111111-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-21111-2-2-1-1-1-1-1-1-1-11111111111110000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-12222-2-2-2-2-1-1-1-1-2-2-1-1-1-111111111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-2-2-2-222221111-2-21111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-122-2-222-2-2-1-1-1-1221111-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-1-2-222-2-222111122-1-1-1-11111-1-1-1-11111-1-1-1-10000000000000000
χ29222-22-2-2-222-2-222-22-22-2-200002i2i−2i−2i2-2000000002-22-22i−2i000022-2-2002i2i−2i−2i000000002i2i−2i−2i00000000000000000000
χ30222-22-2-2-222-2-222-22-22-2-200002i2i−2i−2i2-2000000002-2-22−2i2i0000-2-22200−2i−2i2i2i000000002i2i−2i−2i00000000000000000000
χ31222-22-2-2-222-2-222-22-22-2-20000−2i−2i2i2i2-2000000002-22-2−2i2i000022-2-200−2i−2i2i2i00000000−2i−2i2i2i00000000000000000000
χ32222-22-2-2-222-2-222-22-22-2-20000−2i−2i2i2i2-2000000002-2-222i−2i0000-2-222002i2i−2i−2i00000000−2i−2i2i2i00000000000000000000
χ33222-22-2-2-2-12-2-22-11-11-11100002i2i−2i−2i-1133−3−333−3−3-112-22i−2i0000-1-11100−i−iii−i3−i3i3i333−3−3−i−iii−i3−i3i3i30000000000000000
χ34222-22-2-2-2-12-2-22-11-11-11100002i2i−2i−2i-1133−3−333−3−3-11-22−2i2i000011-1-100ii−i−ii3i3−i3−i3−3−333−i−iii−i3−i3i3i30000000000000000
χ35222-22-2-2-2-12-2-22-11-11-11100002i2i−2i−2i-11−3−333−3−333-112-22i−2i0000-1-11100−i−iiii3i3−i3−i3−3−333−i−iiii3i3−i3−i30000000000000000
χ36222-22-2-2-2-12-2-22-11-11-11100002i2i−2i−2i-11−3−333−3−333-11-22−2i2i000011-1-100ii−i−i−i3−i3i3i333−3−3−i−iiii3i3−i3−i30000000000000000
χ37222-22-2-2-2-12-2-22-11-11-1110000−2i−2i2i2i-1133−3−333−3−3-112-2−2i2i0000-1-11100ii−i−ii3i3−i3−i333−3−3ii−i−ii3i3−i3−i30000000000000000
χ38222-22-2-2-2-12-2-22-11-11-1110000−2i−2i2i2i-1133−3−333−3−3-11-222i−2i000011-1-100−i−iii−i3−i3i3i3−3−333ii−i−ii3i3−i3−i30000000000000000
χ39222-22-2-2-2-12-2-22-11-11-1110000−2i−2i2i2i-11−3−333−3−333-112-2−2i2i0000-1-11100ii−i−i−i3−i3i3i3−3−333ii−i−i−i3−i3i3i30000000000000000
χ40222-22-2-2-2-12-2-22-11-11-1110000−2i−2i2i2i-11−3−333−3−333-11-222i−2i000011-1-100−i−iiii3i3−i3−i333−3−3ii−i−i−i3−i3i3i30000000000000000
χ412-2-222-2-2222-22-2-222-2-22-200002-22-22-200000000-2200002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i2-22-200000000000000000000
χ422-2-222-2-2222-22-2-222-2-22-200002-22-22-200000000-220000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i2-22-200000000000000000000
χ432-2-222-2-2222-22-2-222-2-22-20000-22-222-200000000-2200002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i-22-2200000000000000000000
χ442-2-222-2-2222-22-2-222-2-22-20000-22-222-200000000-220000−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i-22-2200000000000000000000
χ452-2-222-2-22-12-22-21-1-111-1100002-22-2-113−33−33−33−31-100002i−2i2i−2i−i3i3−i3i300−i3i3−i3i3−ii−ii−ii−ii-11-113−33−30000000000000000
χ462-2-222-2-22-12-22-21-1-111-1100002-22-2-113−33−33−33−31-10000−2i2i−2i2ii3−i3i3−i300i3−i3i3−i3i−ii−ii−ii−i-11-113−33−30000000000000000
χ472-2-222-2-22-12-22-21-1-111-1100002-22-2-11−33−33−33−331-100002i−2i2i−2ii3−i3i3−i300i3−i3i3−i3−ii−ii−ii−ii-11-11−33−330000000000000000
χ482-2-222-2-22-12-22-21-1-111-1100002-22-2-11−33−33−33−331-10000−2i2i−2i2i−i3i3−i3i300−i3i3−i3i3i−ii−ii−ii−i-11-11−33−330000000000000000
χ492-2-222-2-22-12-22-21-1-111-110000-22-22-113−33−33−33−31-100002i−2i−2i2ii3−i3i3−i300−i3i3−i3i3−ii−iii−ii−i1-11-1−33−330000000000000000
χ502-2-222-2-22-12-22-21-1-111-110000-22-22-113−33−33−33−31-10000−2i2i2i−2i−i3i3−i3i300i3−i3i3−i3i−ii−i−ii−ii1-11-1−33−330000000000000000
χ512-2-222-2-22-12-22-21-1-111-110000-22-22-11−33−33−33−331-100002i−2i−2i2i−i3i3−i3i300i3−i3i3−i3−ii−iii−ii−i1-11-13−33−30000000000000000
χ522-2-222-2-22-12-22-21-1-111-110000-22-22-11−33−33−33−331-10000−2i2i2i−2ii3−i3i3−i300−i3i3−i3i3i−ii−i−ii−ii1-11-13−33−30000000000000000
χ532-2-2-2222-2222-2-2-2-222-2-222-22-22i−2i−2i2i222-2-222-2-22-2-20000000000002i−2i0000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ542-2-2-2222-2222-2-2-2-222-2-222-22-2−2i2i2i−2i222-2-222-2-22-2-2000000000000−2i2i000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ552-2-2-2222-2222-2-2-2-222-2-22-22-222i−2i−2i2i22-222-2-222-2-2-2000000000000−2i2i0000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ562-2-2-2222-2222-2-2-2-222-2-22-22-22−2i2i2i−2i22-222-2-222-2-2-20000000000002i−2i000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ572-2-2-2222-22-2-222-2-222-2-222-2-220000-2-22-2-22-222-2220000000000000000000000000000000000000022-2-2002-20000
χ582-2-2-2222-22-2-222-2-222-2-222-2-220000-2-22-2-22-222-22200000000000000000000000000000000000000-2-22200-220000
χ592-2-2-2222-22-2-222-2-222-2-22-222-20000-2-2-222-22-2-22220000000000000000000000000000000000000022-2-200-220000
χ602-2-2-2222-22-2-222-2-222-2-22-222-20000-2-2-222-22-2-222200000000000000000000000000000000000000-2-222002-20000
χ612-2-2-2222-2-122-2-211-1-111-12-22-22i−2i−2i2i-1-1-111-1-111-11100000000−i3i3i3−i32i−2i3−3−33−333−3−i3i3i3−i3−iii−ii−i−ii0000000000000000
χ622-2-2-2222-2-122-2-211-1-111-12-22-22i−2i−2i2i-1-1-111-1-111-11100000000i3−i3−i3i32i−2i−333−33−3−33i3−i3−i3i3−iii−ii−i−ii0000000000000000
χ632-2-2-2222-2-122-2-211-1-111-12-22-2−2i2i2i−2i-1-1-111-1-111-11100000000−i3i3i3−i3−2i2i−333−33−3−33−i3i3i3−i3i−i−ii−iii−i0000000000000000
χ642-2-2-2222-2-122-2-211-1-111-12-22-2−2i2i2i−2i-1-1-111-1-111-11100000000i3−i3−i3i3−2i2i3−3−33−333−3i3−i3−i3i3i−i−ii−iii−i0000000000000000
χ652-2-2-2222-2-122-2-211-1-111-1-22-222i−2i−2i2i-1-11-1-111-1-111100000000−i3i3i3−i3−2i2i3−3−333−3−33i3−i3−i3i3−iii−i−iii−i0000000000000000
χ662-2-2-2222-2-122-2-211-1-111-1-22-222i−2i−2i2i-1-11-1-111-1-111100000000i3−i3−i3i3−2i2i−333−3−333−3−i3i3i3−i3−iii−i−iii−i0000000000000000
χ672-2-2-2222-2-122-2-211-1-111-1-22-22−2i2i2i−2i-1-11-1-111-1-111100000000−i3i3i3−i32i−2i−333−3−333−3i3−i3−i3i3i−i−iii−i−ii0000000000000000
χ682-2-2-2222-2-122-2-211-1-111-1-22-22−2i2i2i−2i-1-11-1-111-1-111100000000i3−i3−i3i32i−2i3−3−333−3−33−i3i3i3−i3i−i−iii−i−ii0000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4000022-2-2-2-222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ71444-44-4-4-44-444-44-44-44-4-400000000-4400000000-4400000000000000000000000000000000000000000000000000
χ72444-44-4-4-4-2-444-4-22-22-222000000002-22323−23−23−23−2323232-200000000000000000000000000000000000000000000000000
χ73444-44-4-4-4-2-444-4-22-22-222000000002-2−23−2323232323−23−232-200000000000000000000000000000000000000000000000000
χ7444-44-4-44-4400004-4-4-4-4440000000000000000000000000000000000000000000000000000004i−4i00000000000000
χ7544-44-4-44-4400004-4-4-4-444000000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ7644-4-4-44-444000044-44-4-4-40000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i200000000
χ7744-4-4-44-444000044-44-4-4-400000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i200000000
χ784-444-44-4-440000-4-4-4444-40000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ794-444-44-4-440000-4-4-4444-400000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ804-44-4-4-44440000-44-4-44-44000000000000000000000000000000000000000000000000000000004-4000000000000
χ814-44-4-4-44440000-44-4-44-4400000000000000000000000000000000000000000000000000000000-44000000000000
χ824-4-444-4-444-44-44-444-4-44-400000000-44000000004-400000000000000000000000000000000000000000000000000
χ834-4-444-4-44-2-44-442-2-222-22000000002-223−2323−23−2323−2323-2200000000000000000000000000000000000000000000000000
χ844-4-444-4-44-2-44-442-2-222-22000000002-2−2323−232323−2323−23-2200000000000000000000000000000000000000000000000000
χ854-4-4-4444-4-2-4-44422-2-222-24-4-44000022-222-22-2-22-2-200000000000000000000000000000000000000000000000000
χ864-4-4-4444-4-2-4-44422-2-222-2-444-40000222-2-22-222-2-2-200000000000000000000000000000000000000000000000000
χ8788-88-8-88-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-88-88-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-88-8-8-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-8-888-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000

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