Finite Group Databasebeta

← Group #10883558

Character table — Group #10883558

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222222222444444444444444444444444488888888888888888888888888888888242424242424242448484848
order1222234444666884444668881212121212121212121212122424242422444444666688121212121212121212121212242424242424224488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-11-111-1-111-1-1
χ6111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-11-11-1-111-1-111
χ7111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11-11-111-1-1-1-111
χ8111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-11-11-1-11111-1-1
χ91111111111111-1-1111111-1-1-1111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-1-1-1111-11-1
χ101111111111111-1-1111111-1-1-1111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-11-11
χ111111111111111-1-1111111-1-1-1111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-11-1-1-111-11-11
χ121111111111111-1-1111111-1-1-1111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1111-1-11-11-1
χ131111111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11-1-11
χ141111111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-111-1
χ151111111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-111-1
χ161111111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111111-1-11
χ1722222-12222-1-1-1222222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1822222-12222-1-1-1222222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111122111111111111-1-1-1-1-1-1000000000000
χ1922222-12222-1-1-122-2-2-2-2-1-1222-1-111111111-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-2-2-1-1-1-111111111-1-11111000000000000
χ2022222-12222-1-1-122-2-2-2-2-1-1222-1-111111111-1-1-1-1-1-1-2-2-2-222221111-2-21111-1-1-1-1-1-1-1-1-1-11111000000000000
χ2122222-12222-1-1-1-2-22222-1-1-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111122-2-222-2-2-1-1-1-1-2-21111-1-1-1-11111111111000000000000
χ2222222-12222-1-1-1-2-22222-1-1-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111-2-222-2-2221111-2-2-1-1-1-11111-1-1-1-1111111000000000000
χ2322222-12222-1-1-1-2-2-2-2-2-2-1-1-2-2-2-1-111111111-1-1111122-2-2-2-222-1-1-1-12211111111-1-1-1-111-1-1-1-1000000000000
χ2422222-12222-1-1-1-2-2-2-2-2-2-1-1-2-2-2-1-111111111-1-11111-2-22222-2-2111122-1-1-1-1-1-1-1-1111111-1-1-1-1000000000000
χ25222-2-222-2-222-2-22200002-22-2-22-2000000002-222-2-200002i−2i2i−2i00000000002i2i−2i−2i2i2i−2i−2i2-20000000000000000
χ26222-2-222-2-222-2-22200002-22-2-22-2000000002-222-2-20000−2i2i−2i2i0000000000−2i−2i2i2i−2i−2i2i2i2-20000000000000000
χ27222-2-222-2-222-2-2-2-200002-2-2222-2000000002-2-2-22200002i−2i−2i2i00000000002i2i−2i−2i−2i−2i2i2i-220000000000000000
χ28222-2-222-2-222-2-2-2-200002-2-2222-2000000002-2-2-2220000−2i2i2i−2i0000000000−2i−2i2i2i2i2i−2i−2i-220000000000000000
χ29222-2-22-222-22-2-2002i2i−2i−2i2-2000-222i2i2i2i−2i−2i−2i−2i-22000000000000000000000000000000000000020-22i−2i000000
χ30222-2-22-222-22-2-2002i2i−2i−2i2-2000-222i2i2i2i−2i−2i−2i−2i-220000000000000000000000000000000000000-202−2i2i000000
χ31222-2-22-222-22-2-200−2i−2i2i2i2-2000-22−2i−2i−2i−2i2i2i2i2i-22000000000000000000000000000000000000020-2−2i2i000000
χ32222-2-22-222-22-2-200−2i−2i2i2i2-2000-22−2i−2i−2i−2i2i2i2i2i-220000000000000000000000000000000000000-2022i−2i000000
χ33222-2-2-12-2-22-111220000-112-2-2-1133−3−333−3−3-11-1-11100002i−2i2i−2i−i3−i3i3i300−i3−i3i3i3−i−iii−i−iii-1133−3−3000000000000
χ34222-2-2-12-2-22-111220000-112-2-2-1133−3−333−3−3-11-1-1110000−2i2i−2i2ii3i3−i3−i300i3i3−i3−i3ii−i−iii−i−i-1133−3−3000000000000
χ35222-2-2-12-2-22-111220000-112-2-2-11−3−333−3−333-11-1-11100002i−2i2i−2ii3i3−i3−i300i3i3−i3−i3−i−iii−i−iii-11−3−333000000000000
χ36222-2-2-12-2-22-111220000-112-2-2-11−3−333−3−333-11-1-1110000−2i2i−2i2i−i3−i3i3i300−i3−i3i3i3ii−i−iii−i−i-11−3−333000000000000
χ37222-2-2-12-2-22-111-2-20000-11-222-1133−3−333−3−3-1111-1-100002i−2i−2i2i−i3−i3i3i300i3i3−i3−i3−i−iiiii−i−i1-1−3−333000000000000
χ38222-2-2-12-2-22-111-2-20000-11-222-1133−3−333−3−3-1111-1-10000−2i2i2i−2ii3i3−i3−i300−i3−i3i3i3ii−i−i−i−iii1-1−3−333000000000000
χ39222-2-2-12-2-22-111-2-20000-11-222-11−3−333−3−333-1111-1-100002i−2i−2i2ii3i3−i3−i300−i3−i3i3i3−i−iiiii−i−i1-133−3−3000000000000
χ40222-2-2-12-2-22-111-2-20000-11-222-11−3−333−3−333-1111-1-10000−2i2i2i−2i−i3−i3i3i300i3i3−i3−i3ii−i−i−i−iii1-133−3−3000000000000
χ4122-22-22-22-22222222-22-2-2-2-22-2-2-22-22-22-22-22222220000000000002-2000000000000-2-22-22-2000000000000
χ4222-22-22-22-2222222-22-22-2-2-22-2-2-2-22-22-22-22222222000000000000-22000000000000-2-2-22-22000000000000
χ4322-22-22-22-22222-2-22-22-2-2-22-22-2-22-22-22-22-222-2-2-2-2000000000000-2200000000000022-22-22000000000000
χ4422-22-22-22-22222-2-2-22-22-2-22-22-2-2-22-22-22-2222-2-2-2-20000000000002-2000000000000222-22-2000000000000
χ4522-22-2-1-22-22-1-1-1222-22-211-22-211-11-11-11-11-1-1-1-1-1-100000000−i3i3−i3i32-2−i3i3−i3i3−i3i3−i3i3−i3i3−i3i311-11-11000000000000
χ4622-22-2-1-22-22-1-1-1222-22-211-22-211-11-11-11-11-1-1-1-1-1-100000000i3−i3i3−i32-2i3−i3i3−i3i3−i3i3−i3i3−i3i3−i311-11-11000000000000
χ4722-22-2-1-22-22-1-1-122-22-2211-22-2111-11-11-11-1-1-1-1-1-1-100000000−i3i3−i3i3-22−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3111-11-1000000000000
χ4822-22-2-1-22-22-1-1-122-22-2211-22-2111-11-11-11-1-1-1-1-1-1-100000000i3−i3i3−i3-22i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3111-11-1000000000000
χ4922-22-2-1-22-22-1-1-1-2-22-22-2112-2211-11-11-11-11-1-1111100000000−i3i3−i3i3-22i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3-1-11-11-1000000000000
χ5022-22-2-1-22-22-1-1-1-2-22-22-2112-2211-11-11-11-11-1-1111100000000i3−i3i3−i3-22−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3-1-11-11-1000000000000
χ5122-22-2-1-22-22-1-1-1-2-2-22-22112-22111-11-11-11-1-1-1111100000000−i3i3−i3i32-2i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3-1-1-11-11000000000000
χ5222-22-2-1-22-22-1-1-1-2-2-22-22112-22111-11-11-11-1-1-1111100000000i3−i3i3−i32-2−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3-1-1-11-11000000000000
χ5322-2-22222-2-22-2-2002i−2i−2i2i-220002-22i−2i2i−2i−2i2i−2i2i-2200000000000000000000000000000000000020-20002i−2i0000
χ5422-2-22222-2-22-2-2002i−2i−2i2i-220002-22i−2i2i−2i−2i2i−2i2i-22000000000000000000000000000000000000-202000−2i2i0000
χ5522-2-22222-2-22-2-200−2i2i2i−2i-220002-2−2i2i−2i2i2i−2i2i−2i-2200000000000000000000000000000000000020-2000−2i2i0000
χ5622-2-22222-2-22-2-200−2i2i2i−2i-220002-2−2i2i−2i2i2i−2i2i−2i-22000000000000000000000000000000000000-2020002i−2i0000
χ5722-2-222-2-2222-2-2220000-22-2-22-22000000002-222-2-22-22-200002-2-22002-2-2200000000-220000000000000000
χ5822-2-222-2-2222-2-2220000-22-2-22-22000000002-222-2-2-22-220000-222-200-222-200000000-220000000000000000
χ5922-2-222-2-2222-2-2-2-20000-2222-2-22000000002-2-2-2222-2-2200002-2-2200-222-2000000002-20000000000000000
χ6022-2-222-2-2222-2-2-2-20000-2222-2-22000000002-2-2-222-222-20000-222-2002-2-22000000002-20000000000000000
χ6122-2-22-1-2-222-1112200001-1-2-221-13−3−333−3−33-11-1-1112-22-20000-111-100-111-13−3−333−3−331-13−3−33000000000000
χ6222-2-22-1-2-222-1112200001-1-2-221-13−3−333−3−33-11-1-111-22-2200001-1-11001-1-11−333−3−333−31-13−3−33000000000000
χ6322-2-22-1-2-222-1112200001-1-2-221-1−333−3−333−3-11-1-1112-22-20000-111-100-111-1−333−3−333−31-1−333−3000000000000
χ6422-2-22-1-2-222-1112200001-1-2-221-1−333−3−333−3-11-1-111-22-2200001-1-11001-1-113−3−333−3−331-1−333−3000000000000
χ6522-2-22-1-2-222-111-2-200001-122-21-13−3−333−3−33-1111-1-12-2-220000-111-1001-1-113−3−33−333−3-11−333−3000000000000
χ6622-2-22-1-2-222-111-2-200001-122-21-13−3−333−3−33-1111-1-1-222-200001-1-1100-111-1−333−33−3−33-11−333−3000000000000
χ6722-2-22-1-2-222-111-2-200001-122-21-1−333−3−333−3-1111-1-12-2-220000-111-1001-1-11−333−33−3−33-113−3−33000000000000
χ6822-2-22-1-2-222-111-2-200001-122-21-1−333−3−333−3-1111-1-1-222-200001-1-1100-111-13−3−33−333−3-113−3−33000000000000
χ69444444-4-4-4-444400000044000-4-400000000-4-4000000000000000000000000000000000000000000000000
χ7044444-2-4-4-4-4-2-2-2000000-2-200022−2i3−2i32i32i32i32i3−2i3−2i322000000000000000000000000000000000000000000000000
χ7144444-2-4-4-4-4-2-2-2000000-2-2000222i32i3−2i3−2i3−2i3−2i32i32i322000000000000000000000000000000000000000000000000
χ72444-4-4-2-444-4-222004i4i−4i−4i-220002-2−2i−2i−2i−2i2i2i2i2i2-2000000000000000000000000000000000000000000000000
χ73444-4-4-2-444-4-22200−4i−4i4i4i-220002-22i2i2i2i−2i−2i−2i−2i2-2000000000000000000000000000000000000000000000000
χ7444-44-444-44-4444000000-4-40004400000000-4-4000000000000000000000000000000000000000000000000
χ7544-44-4-24-44-4-2-2-200000022000-2-2−2i32i32i3−2i32i3−2i3−2i32i322000000000000000000000000000000000000000000000000
χ7644-44-4-24-44-4-2-2-200000022000-2-22i3−2i3−2i32i3−2i32i32i3−2i322000000000000000000000000000000000000000000000000
χ7744-4-44-244-4-4-222004i−4i−4i4i2-2000-22−2i2i−2i2i2i−2i2i−2i2-2000000000000000000000000000000000000000000000000
χ7844-4-44-244-4-4-22200−4i4i4i−4i2-2000-222i−2i2i−2i−2i2i−2i2i2-2000000000000000000000000000000000000000000000000
χ798-800080000-800−4i24i2000000000000000000000−4i24i20000000000000000000000000000000000000000000000
χ808-800080000-8004i2−4i20000000000000000000004i2−4i20000000000000000000000000000000000000000000000
χ818-8000-400004−4i34i3−4i24i20000000000000000000002i2−2i226−2600000000000000000000000000000000000000000000
χ828-8000-400004−4i34i34i2−4i2000000000000000000000−2i22i2−262600000000000000000000000000000000000000000000
χ838-8000-4000044i3−4i3−4i24i20000000000000000000002i2−2i2−262600000000000000000000000000000000000000000000
χ848-8000-4000044i3−4i34i2−4i2000000000000000000000−2i22i226−2600000000000000000000000000000000000000000000

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