Finite Group Databasebeta

← Group #10876109

Character table — Group #10876109

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order12222222344446666666222244441212121212121212121212124444446666888812121212121212121212121224242424242424244444444444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1111-1-1-1-111-11
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-11111-1-11-1
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1111-1-111-1-11-1
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-111-1-111-11
χ911111111111111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ1111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1
χ1211111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-1-11-1-11111-1-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1111-111-1-1-1-1111-1
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-11-1-111-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1111-111-1-111-1-1-11
χ17222222222-2-2-2-22222222000022-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000002222-2-20000000000
χ18222222222-2-2-2-22222222000022-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000-2-2-2-2220000000000
χ19222222222-2-2-2-222222220000-2-222-2-22222-2-2-2-2-2-2000000000000000000000000000000000022-2-22-20000000000
χ20222222222-2-2-2-222222220000-2-222-2-22222-2-2-2-2-2-20000000000000000000000000000000000-2-222-220000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1-2-2-2-211111111-1-1-1-1111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-122-2-2-2-2-1-1-1-1-2-222-1-1-1-111111111-1-1-1-111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-2-2-2-222-1-1-1-122-2-21111-1-1-1-111111111-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-122-2-2221111-2-2-2-2-1-1-1-1-1-1-1-11111111111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211112222111111111111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-12222-2-2111122-2-2-1-1-1-11111-1-1-1-11111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-1-2-222221111-2-2221111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ29222-22-2-2-22-2-2222-22-22-2-222-2-200002-2000000002-200002i−2i22-2-22i−2i0000002i2i−2i−2i000000002i2i−2i−2i0000000000000000
χ30222-22-2-2-22-2-2222-22-22-2-222-2-200002-2000000002-20000−2i2i22-2-2−2i2i000000−2i−2i2i2i00000000−2i−2i2i2i0000000000000000
χ31222-22-2-2-22-2-2222-22-22-2-2-2-22200002-2000000002-200002i−2i-2-222−2i2i0000002i2i−2i−2i00000000−2i−2i2i2i0000000000000000
χ32222-22-2-2-22-2-2222-22-22-2-2-2-22200002-2000000002-20000−2i2i-2-2222i−2i000000−2i−2i2i2i000000002i2i−2i−2i0000000000000000
χ33222-22-2-2-2-1-2-222-11-11-11122-2-20000-1133−3−333−3−3-1100002i−2i-1-1112i−2i00−i3−i3i3i3−i−iii33−3−3−i3−i3i3i3−i−iii0000000000000000
χ34222-22-2-2-2-1-2-222-11-11-11122-2-20000-1133−3−333−3−3-110000−2i2i-1-111−2i2i00i3i3−i3−i3ii−i−i33−3−3i3i3−i3−i3ii−i−i0000000000000000
χ35222-22-2-2-2-1-2-222-11-11-11122-2-20000-11−3−333−3−333-1100002i−2i-1-1112i−2i00i3i3−i3−i3−i−iii−3−333i3i3−i3−i3−i−iii0000000000000000
χ36222-22-2-2-2-1-2-222-11-11-11122-2-20000-11−3−333−3−333-110000−2i2i-1-111−2i2i00−i3−i3i3i3ii−i−i−3−333−i3−i3i3i3ii−i−i0000000000000000
χ37222-22-2-2-2-1-2-222-11-11-111-2-2220000-1133−3−333−3−3-1100002i−2i11-1-1−2i2i00−i3−i3i3i3−i−iii−3−333i3i3−i3−i3ii−i−i0000000000000000
χ38222-22-2-2-2-1-2-222-11-11-111-2-2220000-1133−3−333−3−3-110000−2i2i11-1-12i−2i00i3i3−i3−i3ii−i−i−3−333−i3−i3i3i3−i−iii0000000000000000
χ39222-22-2-2-2-1-2-222-11-11-111-2-2220000-11−3−333−3−333-1100002i−2i11-1-1−2i2i00i3i3−i3−i3−i−iii33−3−3−i3−i3i3i3ii−i−i0000000000000000
χ40222-22-2-2-2-1-2-222-11-11-111-2-2220000-11−3−333−3−333-110000−2i2i11-1-12i−2i00−i3−i3i3i3ii−i−i33−3−3i3i3−i3−i3−i−iii0000000000000000
χ4122-22-2-2-2222-2-22-222-2-22-200002i−2i2i−2i-222i−2i2i−2i2i−2i2i−2i2-200000000000000000000000000000000000000002i−2i2-2000000
χ4222-22-2-2-2222-2-22-222-2-22-200002i−2i2i−2i-222i−2i2i−2i2i−2i2i−2i2-20000000000000000000000000000000000000000−2i2i-22000000
χ4322-22-2-2-2222-2-22-222-2-22-20000−2i2i−2i2i-22−2i2i−2i2i−2i2i−2i2i2-200000000000000000000000000000000000000002i−2i-22000000
χ4422-22-2-2-2222-2-22-222-2-22-20000−2i2i−2i2i-22−2i2i−2i2i−2i2i−2i2i2-20000000000000000000000000000000000000000−2i2i2-2000000
χ4522-22-2-2-222-222-2-222-2-22-22-22-22i−2i−2i2i2-2−2i2i−2i2i2i−2i2i−2i-22002i−2i002-22-20000000000002i−2i2i−2i000000000000000000000000
χ4622-22-2-2-222-222-2-222-2-22-22-22-2−2i2i2i−2i2-22i−2i2i−2i−2i2i−2i2i-2200−2i2i002-22-2000000000000−2i2i−2i2i000000000000000000000000
χ4722-22-2-2-222-222-2-222-2-22-2-22-222i−2i−2i2i2-2−2i2i−2i2i2i−2i2i−2i-2200−2i2i00-22-22000000000000−2i2i−2i2i000000000000000000000000
χ4822-22-2-2-222-222-2-222-2-22-2-22-22−2i2i2i−2i2-22i−2i2i−2i−2i2i−2i2i-22002i−2i00-22-220000000000002i−2i2i−2i000000000000000000000000
χ4922-22-2-2-22-1-222-21-1-111-112-22-22i−2i−2i2i-11i−ii−i−ii−ii1-1002i−2i00-11-1100003−33−3−i3i3−i3i3−ii−ii3−33−3−i3i3−i3i30000000000000000
χ5022-22-2-2-22-1-222-21-1-111-112-22-22i−2i−2i2i-11i−ii−i−ii−ii1-1002i−2i00-11-110000−33−33i3−i3i3−i3−ii−ii−33−33i3−i3i3−i30000000000000000
χ5122-22-2-2-22-1-222-21-1-111-112-22-2−2i2i2i−2i-11−ii−iii−ii−i1-100−2i2i00-11-1100003−33−3i3−i3i3−i3i−ii−i3−33−3i3−i3i3−i30000000000000000
χ5222-22-2-2-22-1-222-21-1-111-112-22-2−2i2i2i−2i-11−ii−iii−ii−i1-100−2i2i00-11-110000−33−33−i3i3−i3i3i−ii−i−33−33−i3i3−i3i30000000000000000
χ5322-22-2-2-22-1-222-21-1-111-11-22-222i−2i−2i2i-11i−ii−i−ii−ii1-100−2i2i001-11-100003−33−3−i3i3−i3i3i−ii−i−33−33i3−i3i3−i30000000000000000
χ5422-22-2-2-22-1-222-21-1-111-11-22-222i−2i−2i2i-11i−ii−i−ii−ii1-100−2i2i001-11-10000−33−33i3−i3i3−i3i−ii−i3−33−3−i3i3−i3i30000000000000000
χ5522-22-2-2-22-1-222-21-1-111-11-22-22−2i2i2i−2i-11−ii−iii−ii−i1-1002i−2i001-11-100003−33−3i3−i3i3−i3−ii−ii−33−33−i3i3−i3i30000000000000000
χ5622-22-2-2-22-1-222-21-1-111-11-22-22−2i2i2i−2i-11−ii−iii−ii−i1-1002i−2i001-11-10000−33−33−i3i3−i3i3−ii−ii3−33−3i3−i3i3−i30000000000000000
χ5722-2-2-222-222-22-2-2-222-2-222-2-2200002200000000-2-22i−2i00002-2-22002i−2i2i−2i−2i2i000000002i−2i−2i2i00000000000000000000
χ5822-2-2-222-222-22-2-2-222-2-222-2-2200002200000000-2-2−2i2i00002-2-2200−2i2i−2i2i2i−2i00000000−2i2i2i−2i00000000000000000000
χ5922-2-2-222-222-22-2-2-222-2-22-222-200002200000000-2-22i−2i0000-222-200−2i2i2i−2i−2i2i00000000−2i2i2i−2i00000000000000000000
χ6022-2-2-222-222-22-2-2-222-2-22-222-200002200000000-2-2−2i2i0000-222-2002i−2i−2i2i2i−2i000000002i−2i−2i2i00000000000000000000
χ6122-2-2-222-2-12-22-211-1-111-12-2-220000-1-1−i3i3i3−i3i3−i3−i3i3112i−2i0000-111-1002i−2i−iii−i3−3−33i3−i3−i3i3−iii−i3−3−330000000000000000
χ6222-2-2-222-2-12-22-211-1-111-12-2-220000-1-1−i3i3i3−i3i3−i3−i3i311−2i2i0000-111-100−2i2ii−i−ii−333−3i3−i3−i3i3i−i−ii−333−30000000000000000
χ6322-2-2-222-2-12-22-211-1-111-12-2-220000-1-1i3−i3−i3i3−i3i3i3−i3112i−2i0000-111-1002i−2i−iii−i−333−3−i3i3i3−i3−iii−i−333−30000000000000000
χ6422-2-2-222-2-12-22-211-1-111-12-2-220000-1-1i3−i3−i3i3−i3i3i3−i311−2i2i0000-111-100−2i2ii−i−ii3−3−33−i3i3i3−i3i−i−ii3−3−330000000000000000
χ6522-2-2-222-2-12-22-211-1-111-1-222-20000-1-1−i3i3i3−i3i3−i3−i3i3112i−2i00001-1-1100−2i2i−iii−i3−3−33−i3i3i3−i3i−i−ii−333−30000000000000000
χ6622-2-2-222-2-12-22-211-1-111-1-222-20000-1-1−i3i3i3−i3i3−i3−i3i311−2i2i00001-1-11002i−2ii−i−ii−333−3−i3i3i3−i3−iii−i3−3−330000000000000000
χ6722-2-2-222-2-12-22-211-1-111-1-222-20000-1-1i3−i3−i3i3−i3i3i3−i3112i−2i00001-1-1100−2i2i−iii−i−333−3i3−i3−i3i3i−i−ii3−3−330000000000000000
χ6822-2-2-222-2-12-22-211-1-111-1-222-20000-1-1i3−i3−i3i3−i3i3i3−i311−2i2i00001-1-11002i−2ii−i−ii3−3−33i3−i3−i3i3−iii−i−333−30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-4222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-44422-2-2-2-222222200000000000000000000000000000000000000000000000000
χ71444-44-4-4-4444-4-44-44-44-4-400000000-4400000000-4400000000000000000000000000000000000000000000000000
χ72444-44-4-4-4-244-4-4-22-22-222000000002-22323−23−23−23−2323232-200000000000000000000000000000000000000000000000000
χ73444-44-4-4-4-244-4-4-22-22-222000000002-2−23−2323232323−23−232-200000000000000000000000000000000000000000000000000
χ7444-44-4-4-44-24-4-442-2-222-2200004i−4i4i−4i2-2−2i2i−2i2i−2i2i−2i2i-2200000000000000000000000000000000000000000000000000
χ7544-44-4-4-44-24-4-442-2-222-220000−4i4i−4i4i2-22i−2i2i−2i2i−2i2i−2i-2200000000000000000000000000000000000000000000000000
χ7644-4-4-444-44-44-44-4-444-4-4400000000-4-4000000004400000000000000000000000000000000000000000000000000
χ7744-4-4-444-4-2-44-4422-2-222-20000000022−2i32i32i3−2i3−2i32i32i3−2i3-2-200000000000000000000000000000000000000000000000000
χ7844-4-4-444-4-2-44-4422-2-222-200000000222i3−2i3−2i32i32i3−2i3−2i32i3-2-200000000000000000000000000000000000000000000000000
χ794-444-44-4-440000-44-4-44-440000000000000000000000000000000000000000000000000000004i−4i00000000000000
χ804-444-44-4-440000-44-4-44-44000000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ814-44-4-4-44440000-4-4-4444-4000000000000000000000000000000000000000000000000000000000000000022−220000
χ824-44-4-4-44440000-4-4-4444-40000000000000000000000000000000000000000000000000000000000000000−22220000
χ834-4-444-44-44000044-44-4-4-4000000000000000000000000000000000000000000000000000000004i−4i000000000000
χ844-4-444-44-44000044-44-4-4-400000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ854-4-4-444-44400004-4-4-4-44400000000000000000000000000000000000000000000000000000000000000000022−2200
χ864-4-4-444-44400004-4-4-4-444000000000000000000000000000000000000000000000000000000000000000000−222200
χ878-888-88-8-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ888-88-8-8-888-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ898-8-888-88-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-88-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000000000

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