Finite Group Databasebeta

← Group #10712201

Character table — Group #10712201

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222222222444444444444444444444444488888888888888888888888888888888242424242424242448484848
order122223444466688224466666688812121212121212122424242444444444881212121212121212121212121212121224242424242416161616161616162488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ9111-1-11-1-1111-1-1-1-11-11-11-111-1-111-11-1-111-1-1111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1ii−i−iii−i−i1-11-1
χ10111-1-11-1-1111-1-1-1-11-11-11-111-1-111-11-1-111-1-1111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1−i−iii−i−iii-11-11
χ11111-1-11-1-1111-1-1-1-11-11-11-111-1-111-11-1-111-1-1111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1ii−i−iii−i−i-11-11
χ12111-1-11-1-1111-1-1-1-11-11-11-111-1-111-11-1-111-1-1111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−i−iii−i−iii1-11-1
χ13111-1-11-1-1111-1-1-1-1-11-111-1-1-11111-11-1-1-1-111111-1-1ii−i−i−i−iii-11iiii−i−i−i−i−i−i−i−iiiii1-1-1-111ii−i−i−i−iii1-1-11
χ14111-1-11-1-1111-1-1-1-1-11-111-1-1-11111-11-1-1-1-111111-1-1ii−i−i−i−iii-11iiii−i−i−i−i−i−i−i−iiiii1-1-1-111−i−iiiii−i−i-111-1
χ15111-1-11-1-1111-1-1-1-1-11-111-1-1-11111-11-1-1-1-111111-1-1−i−iiiii−i−i-11−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111ii−i−i−i−iii-111-1
χ16111-1-11-1-1111-1-1-1-1-11-111-1-1-11111-11-1-1-1-111111-1-1−i−iiiii−i−i-11−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111−i−iiiii−i−i1-1-11
χ172222222222222-2-22222222222-2-2-222222222-2-2-2-200000000-2-20000000000000000-2-2-2-2-2-2000000000000
χ182222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2222-2-2-2-22-2-2-2-200000000220000000000000000-2-22222000000000000
χ1922222-12222-1-1-1222222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2022222-12222-1-1-1222222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2221111111111111111-1-1-1-1-1-1000000000000
χ2122222-12222-1-1-122-2-2-2-2-1-11111222-1-1-11111-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-1-11111000000000000
χ2222222-12222-1-1-122-2-2-2-2-1-11111222-1-1-11111-1-1-1-1-1-2-2-2-22222-2-211111111-1-1-1-1-1-1-1-1-1-11111000000000000
χ2322222-12222-1-1-1-2-22222-1-1-1-1-1-1-2-2-2-1-1-1-1-1-1-1-1111100000000-2-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3111111000000000000
χ2422222-12222-1-1-1-2-22222-1-1-1-1-1-1-2-2-2-1-1-1-1-1-1-1-1111100000000-2-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3111111000000000000
χ2522222-12222-1-1-1-2-2-2-2-2-2-1-11111-2-2-2-1-1-11111-111110000000022−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-1-1-1000000000000
χ2622222-12222-1-1-1-2-2-2-2-2-2-1-11111-2-2-2-1-1-11111-111110000000022i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-1-1-1000000000000
χ27222-2-22-2-2222-2-2222-22-22-222-2-2-2-222-2-222-2-22-2-22200000000-220000000000000000-22-2-222000000000000
χ28222-2-22-2-2222-2-222-22-222-2-2-222-2-222-2-2-2-2222-2-222000000002-20000000000000000-2222-2-2000000000000
χ29222-2-2-1-2-222-111222-22-2-11-1-111-2-22-111-1-111-111-1-100000000-2233−3−3−3−33333−3−3−3−3331-111-1-1000000000000
χ30222-2-2-1-2-222-111222-22-2-11-1-111-2-22-111-1-111-111-1-100000000-22−3−33333−3−3−3−33333−3−31-111-1-1000000000000
χ31222-2-2-1-2-222-11122-22-22-1111-1-1-2-22-11111-1-1-111-1-1000000002-233−3−3−3−333−3−33333−3−31-1-1-111000000000000
χ32222-2-2-1-2-222-11122-22-22-1111-1-1-2-22-11111-1-1-111-1-1000000002-2−3−33333−3−333−3−3−3−3331-1-1-111000000000000
χ33222-2-2-1-2-222-111-2-22-22-2-11-1-11122-2-111-1-111-1-1-1112i2i−2i−2i2i2i−2i−2i2-2−i−i−i−iiiii−i−i−i−iiiii-11-1-111000000000000
χ34222-2-2-1-2-222-111-2-22-22-2-11-1-11122-2-111-1-111-1-1-111−2i−2i2i2i−2i−2i2i2i2-2iiii−i−i−i−iiiii−i−i−i−i-11-1-111000000000000
χ35222-2-2-1-2-222-111-2-2-22-22-1111-1-122-2-11111-1-1-1-1-1112i2i−2i−2i−2i−2i2i2i-22−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1000000000000
χ36222-2-2-1-2-222-111-2-2-22-22-1111-1-122-2-11111-1-1-1-1-111−2i−2i2i2i2i2i−2i−2i-22iiii−i−i−i−i−i−i−i−iiiii-1111-1-1000000000000
χ3722-22-222-22-22-2-2220000-2200002-2-2-22-200002-2-22200002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i2-20000000000000000
χ3822-22-222-22-22-2-2220000-2200002-2-2-22-200002-2-2220000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i2-20000000000000000
χ3922-22-222-22-22-2-2-2-20000-220000-222-22-20000222-2-22i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i00000000-220000000000000000
χ4022-22-222-22-22-2-2-2-20000-220000-222-22-20000222-2-2−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i00000000-220000000000000000
χ4122-22-22-22-222-2-2002-2-22-2222-2-20002-22-2-222-2000000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ4222-22-22-22-222-2-2002-2-22-2222-2-20002-22-2-222-2000000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ4322-22-22-22-222-2-200-222-2-22-2-2220002-2222-2-2-2000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ4422-22-22-22-222-2-200-222-2-22-2-2220002-2222-2-2-2000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ4522-22-2-12-22-2-1112200001-1−i3i3−i3i32-2-21-11−i3i3−i3i3-111-1-100002i−2i2i−2i003−3−333−3−33−ii−ii−ii−ii-11−i3i3−i3i3000000000000
χ4622-22-2-12-22-2-1112200001-1−i3i3−i3i32-2-21-11−i3i3−i3i3-111-1-10000−2i2i−2i2i00−333−3−333−3i−ii−ii−ii−i-11−i3i3−i3i3000000000000
χ4722-22-2-12-22-2-1112200001-1i3−i3i3−i32-2-21-11i3−i3i3−i3-111-1-100002i−2i2i−2i00−333−3−333−3−ii−ii−ii−ii-11i3−i3i3−i3000000000000
χ4822-22-2-12-22-2-1112200001-1i3−i3i3−i32-2-21-11i3−i3i3−i3-111-1-10000−2i2i−2i2i003−3−333−3−33i−ii−ii−ii−i-11i3−i3i3−i3000000000000
χ4922-22-2-12-22-2-111-2-200001-1−i3i3−i3i3-2221-11−i3i3−i3i3-1-1-1112i−2i2i−2i000000−ii−ii−ii−ii3−3−333−3−331-1i3−i3i3−i3000000000000
χ5022-22-2-12-22-2-111-2-200001-1−i3i3−i3i3-2221-11−i3i3−i3i3-1-1-111−2i2i−2i2i000000i−ii−ii−ii−i−333−3−333−31-1i3−i3i3−i3000000000000
χ5122-22-2-12-22-2-111-2-200001-1i3−i3i3−i3-2221-11i3−i3i3−i3-1-1-1112i−2i2i−2i000000−ii−ii−ii−ii−333−3−333−31-1−i3i3−i3i3000000000000
χ5222-22-2-12-22-2-111-2-200001-1i3−i3i3−i3-2221-11i3−i3i3−i3-1-1-111−2i2i−2i2i000000i−ii−ii−ii−i3−3−333−3−331-1−i3i3−i3i3000000000000
χ5322-2-2222-2-222220022-2-2-2-2222200022-2-2-2-2-2-20000000000000000000000000000000000002−2−222−2−220000
χ5422-2-2222-2-222220022-2-2-2-2222200022-2-2-2-2-2-2000000000000000000000000000000000000−222−2−222−20000
χ5522-2-2222-2-2222200-2-222-2-2-2-2-2-200022-22222-20000000000000000000000000000000000002−2−22−222−20000
χ5622-2-2222-2-2222200-2-222-2-2-2-2-2-200022-22222-2000000000000000000000000000000000000−222−22−2−220000
χ5722-2-222-222-2222220000-2-20000-22-2-2-220000222222-2-220000002-22-2-22-2200000000-2-20000000000000000
χ5822-2-222-222-2222220000-2-20000-22-2-2-22000022222-222-2000000-22-222-22-200000000-2-20000000000000000
χ5922-2-222-222-2222-2-20000-2-200002-22-2-2200002-2-2-2-200002-2-2200000000002-22-2-22-22220000000000000000
χ6022-2-222-222-2222-2-20000-2-200002-22-2-2200002-2-2-2-20000-222-20000000000-22-222-22-2220000000000000000
χ6122-2-22-1-222-2-1-1-122000011−i3i3i3−i3-22-211-1−i3i3i3−i3-1-1-1-1-12-2-22000000-11-111-11-1−i3i3i3−i3i3−i3−i3i311i3−i3−i3i3000000000000
χ6222-2-22-1-222-2-1-1-122000011−i3i3i3−i3-22-211-1−i3i3i3−i3-1-1-1-1-1-222-20000001-11-1-11-11i3−i3−i3i3−i3i3i3−i311i3−i3−i3i3000000000000
χ6322-2-22-1-222-2-1-1-122000011i3−i3−i3i3-22-211-1i3−i3−i3i3-1-1-1-1-12-2-22000000-11-111-11-1i3−i3−i3i3−i3i3i3−i311−i3i3i3−i3000000000000
χ6422-2-22-1-222-2-1-1-122000011i3−i3−i3i3-22-211-1i3−i3−i3i3-1-1-1-1-1-222-20000001-11-1-11-11−i3i3i3−i3i3−i3−i3i311−i3i3i3−i3000000000000
χ6522-2-22-1-222-2-1-1-1-2-2000011−i3i3i3−i32-2211-1−i3i3i3−i3-1111100002-2-2200−i3i3i3−i3i3−i3−i3i3-11-111-11-1-1-1−i3i3i3−i3000000000000
χ6622-2-22-1-222-2-1-1-1-2-2000011−i3i3i3−i32-2211-1−i3i3i3−i3-111110000-222-200i3−i3−i3i3−i3i3i3−i31-11-1-11-11-1-1−i3i3i3−i3000000000000
χ6722-2-22-1-222-2-1-1-1-2-2000011i3−i3−i3i32-2211-1i3−i3−i3i3-1111100002-2-2200i3−i3−i3i3−i3i3i3−i3-11-111-11-1-1-1i3−i3−i3i3000000000000
χ6822-2-22-1-222-2-1-1-1-2-2000011i3−i3−i3i32-2211-1i3−i3−i3i3-111110000-222-200−i3i3i3−i3i3−i3−i3i31-11-1-11-11-1-1i3−i3−i3i3000000000000
χ69444444-4-4-4-4444000000440000000-4-4-40000-4000000000000000000000000000000000000000000000000
χ7044444-2-4-4-4-4-2-2-2000000-2-2−2i32i32i3−2i30002222i3−2i3−2i32i32000000000000000000000000000000000000000000000000
χ7144444-2-4-4-4-4-2-2-2000000-2-22i3−2i3−2i32i3000222−2i32i32i3−2i32000000000000000000000000000000000000000000000000
χ72444-4-4444-4-44-4-40000004-40000000-4440000-4000000000000000000000000000000000000000000000000
χ73444-4-4-244-4-4-222000000-22−2i32i3−2i32i30002-2-22i3−2i32i3−2i32000000000000000000000000000000000000000000000000
χ74444-4-4-244-4-4-222000000-222i3−2i32i3−2i30002-2-2−2i32i3−2i32i32000000000000000000000000000000000000000000000000
χ7544-44-4-2-44-44-222004-4-442-2-2-222000-22-222-2-22000000000000000000000000000000000000000000000000
χ7644-44-4-2-44-44-22200-444-42-222-2-2000-22-2-2-2222000000000000000000000000000000000000000000000000
χ7744-4-44-24-4-44-2-2-20044-4-422-2-2-2-2000-2-2222222000000000000000000000000000000000000000000000000
χ7844-4-44-24-4-44-2-2-200-4-444222222000-2-22-2-2-2-22000000000000000000000000000000000000000000000000
χ798-800080000-800−4i24i200000000000000000000000−4i24i200000000000000000000000000000000000000000000
χ808-800080000-8004i2−4i2000000000000000000000004i2−4i200000000000000000000000000000000000000000000
χ818-8000-400004−4i34i3−4i24i200000000000000000000026−262i2−2i200000000000000000000000000000000000000000000
χ828-8000-400004−4i34i34i2−4i2000000000000000000000−2626−2i22i200000000000000000000000000000000000000000000
χ838-8000-4000044i3−4i3−4i24i2000000000000000000000−26262i2−2i200000000000000000000000000000000000000000000
χ848-8000-4000044i3−4i34i2−4i200000000000000000000026−26−2i22i200000000000000000000000000000000000000000000

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