Finite Group Databasebeta

← Group #10590572

Character table — Group #10590572

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222233334444444444444466666666668888888812121212121212121212121212121818181824243636
order122233446666664444344666121212121212121222888812121212121212121212121244446612121212242424248888121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-11111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ41111111111111111111-1-11111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-111111111111111-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-1-1-11-1-11111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111-1-1-1-11-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1111111-1-1
χ911-1-111-111-1-11-1-111-1-11i−i-11-1-1ii−i−i1-111-111-1-111-1-1i−i1-1ii−i−ii−ii−i1-1ii−i−i11-1-111-1-1i−ii−i
χ1011-1-111-111-1-11-1-111-1-11i−i-11-1-1ii−i−i1-111-1-1-11111-1-1i−i1-1ii−i−ii−i−ii1-1ii−i−i-1-111-1-111−ii−ii
χ1111-1-111-111-1-11-1-111-1-11−ii-11-1-1−i−iii1-111-111-1-111-1-1−ii1-1−i−iii−ii−ii1-1−i−iii11-1-111-1-1−ii−ii
χ1211-1-111-111-1-11-1-111-1-11−ii-11-1-1−i−iii1-111-1-1-11111-1-1−ii1-1−i−iii−iii−i1-1−i−iii-1-111-1-111i−ii−i
χ1311-1-111-111-1-11-1-1-1-1111i−i-11-1-1ii−i−i1-11-1111-1-1-1-111i−i1-1ii−i−i−iii−i-11−i−iii11-1-1-1-111i−i−ii
χ1411-1-111-111-1-11-1-1-1-1111i−i-11-1-1ii−i−i1-11-11-1-111-1-111i−i1-1ii−i−i−ii−ii-11−i−iii-1-11111-1-1−iii−i
χ1511-1-111-111-1-11-1-1-1-1111−ii-11-1-1−i−iii1-11-1111-1-1-1-111−ii1-1−i−iiii−i−ii-11ii−i−i11-1-1-1-111−iii−i
χ1611-1-111-111-1-11-1-1-1-1111−ii-11-1-1−i−iii1-11-11-1-111-1-111−ii1-1−i−iiii−ii−i-11ii−i−i-1-11111-1-1i−i−ii
χ17222222-2-22222222222200222-20000-2-2-2-2-20000222200-2-200000000-2-20000000000000000
χ18222222-2-2222222-2-2-2-2200222-20000-2-2-2220000-2-2-2-200-2-200000000220000000000000000
χ1922222-12222-1-12-12222-122-1-1-12-1-1-1-1-1-12220000-1-1-1-122-1-1-1-1-1-12200-1-1-1-1-1-1000000000000
χ2022222-12222-1-12-12222-1-2-2-1-1-121111-1-12220000-1-1-1-1-2-2-1-11111-2-200-1-11111000000000000
χ2122222-12222-1-12-1-2-2-2-2-122-1-1-12-1-1-1-1-1-12-2-20000111122-1-1-1-1-1-1-2-200111111000000000000
χ2222222-12222-1-12-1-2-2-2-2-1-2-2-1-1-121111-1-12-2-200001111-2-2-1-11111220011-1-1-1-1000000000000
χ2322222-1-2-222-1-12-12222-100-1-1-1-2−i3i3−i3i311-2-2-20000-1-1-1-10011−i3i3−i3i3000011−i3i3−i3i3000000000000
χ2422222-1-2-222-1-12-12222-100-1-1-1-2i3−i3i3−i311-2-2-20000-1-1-1-10011i3−i3i3−i3000011i3−i3i3−i3000000000000
χ2522222-1-2-222-1-12-1-2-2-2-2-100-1-1-1-2−i3i3−i3i311-222000011110011−i3i3−i3i30000-1-1i3−i3i3−i3000000000000
χ2622222-1-2-222-1-12-1-2-2-2-2-100-1-1-1-2i3−i3i3−i311-222000011110011i3−i3i3−i30000-1-1−i3i3−i3i3000000000000
χ272222-1222-1-122-120000-122-1-1-1-1222222-10022220000-1-1-1-1-1-1-1-10022000000-1-1-1-10000-1-100
χ282222-1222-1-122-120000-122-1-1-1-1222222-100-2-2-2-20000-1-1-1-1-1-1-1-100-2-2000000111100001100
χ292222-1222-1-122-120000-1-2-2-1-1-1-1-2-2-2-222-1002222000011-1-1111100-2-2000000-1-1-1-100001100
χ302222-1222-1-122-120000-1-2-2-1-1-1-1-2-2-2-222-100-2-2-2-2000011-1-11111002200000011110000-1-100
χ3122-2-2222-22-2-22-2-222-2-2200-22-220000-22-2-22000022-2-200-2200000000-220000000000000000
χ3222-2-2222-22-2-22-2-2-2-222200-22-220000-22-22-20000-2-22200-22000000002-20000000000000000
χ3322-2-22-12-22-21-1-2122-2-2-1001-1123−3−331-1-2-220000-1-111001-13−3−3300001-13−3−33000000000000
χ3422-2-22-12-22-21-1-2122-2-2-1001-112−333−31-1-2-220000-1-111001-1−333−300001-1−333−3000000000000
χ3522-2-22-12-22-21-1-21-2-222-1001-1123−3−331-1-22-2000011-1-1001-13−3−330000-11−333−3000000000000
χ3622-2-22-12-22-21-1-21-2-222-1001-112−333−31-1-22-2000011-1-1001-1−333−30000-113−3−33000000000000
χ3722-2-22-1-222-21-1-2122-2-2-12i−2i1-11-2−i−iii-1122-20000-1-1112i−2i-11−i−iii2i−2i00-11−i−iii000000000000
χ3822-2-22-1-222-21-1-2122-2-2-1−2i2i1-11-2ii−i−i-1122-20000-1-111−2i2i-11ii−i−i−2i2i00-11ii−i−i000000000000
χ3922-2-22-1-222-21-1-21-2-222-12i−2i1-11-2−i−iii-112-22000011-1-12i−2i-11−i−iii−2i2i001-1ii−i−i000000000000
χ4022-2-22-1-222-21-1-21-2-222-1−2i2i1-11-2ii−i−i-112-22000011-1-1−2i2i-11ii−i−i2i−2i001-1−i−iii000000000000
χ4122-2-2-12-22-11-221-20000-12i−2i1-1112i2i−2i−2i2-2-10022-2-20000−ii-11−i−iii002i−2i000000-1-1110000−ii00
χ4222-2-2-12-22-11-221-20000-12i−2i1-1112i2i−2i−2i2-2-100-2-2220000−ii-11−i−iii00−2i2i00000011-1-10000i−i00
χ4322-2-2-12-22-11-221-20000-1−2i2i1-111−2i−2i2i2i2-2-10022-2-20000i−i-11ii−i−i00−2i2i000000-1-1110000i−i00
χ4422-2-2-12-22-11-221-20000-1−2i2i1-111−2i−2i2i2i2-2-100-2-2220000i−i-11ii−i−i002i−2i00000011-1-10000−ii00
χ452-22-22200-2-2-2-2222i−2i2i−2i2002-2-20000000000−i2i2−i2i22i−2i2i−2i000000000000000000−i2i2−i2i22−22−20000
χ462-22-22200-2-2-2-2222i−2i2i−2i2002-2-20000000000i2−i2i2−i22i−2i2i−2i000000000000000000i2−i2i2−i2−22−220000
χ472-22-22200-2-2-2-222−2i2i−2i2i2002-2-20000000000−i2i2−i2i2−2i2i−2i2i000000000000000000−i2i2−i2i2−22−220000
χ482-22-22200-2-2-2-222−2i2i−2i2i2002-2-20000000000i2−i2i2−i2−2i2i−2i2i000000000000000000i2−i2i2−i22−22−20000
χ492-2-222200-222-2-2-22i−2i−2i2i200-2-220000000000−i2i2i2−i22i−2i−2i2i000000000000000000−i2i2i2−i22−2−220000
χ502-2-222200-222-2-2-22i−2i−2i2i200-2-220000000000i2−i2−i2i22i−2i−2i2i000000000000000000i2−i2−i2i2−222−20000
χ512-2-222200-222-2-2-2−2i2i2i−2i200-2-220000000000−i2i2i2−i2−2i2i2i−2i000000000000000000−i2i2i2−i2−222−20000
χ522-2-222200-222-2-2-2−2i2i2i−2i200-2-220000000000i2−i2−i2i2−2i2i2i−2i000000000000000000i2−i2−i2i22−2−220000
χ534444-24-4-4-2-244-240000-200-2-2-220000-4-420000000000002200000000000000000000000000
χ544444-2-244-2-2-2-2-2-20000144111-2-2-2-2-2-2-2-20000000000-2-21111110000000000000000000000
χ554444-2-244-2-2-2-2-2-200001-4-4111-22222-2-2-200000000002211-1-1-1-10000000000000000000000
χ564444-2-2-4-4-2-2-2-2-2-200001001112−2i32i3−2i32i3222000000000000-1-1i3−i3i3−i30000000000000000000000
χ574444-2-2-4-4-2-2-2-2-2-2000010011122i3−2i32i3−2i3222000000000000-1-1−i3i3−i3i30000000000000000000000
χ5844-4-4-244-4-22-442-40000-2002-22-20000-4420000000000002-200000000000000000000000000
χ5944-4-4-2-24-4-222-2220000100-11-1-223−23−23232-22000000000000-11−333−30000000000000000000000
χ6044-4-4-2-24-4-222-2220000100-11-1-2−232323−232-22000000000000-113−3−330000000000000000000000
χ6144-4-4-2-2-44-222-222000014i−4i-11-12−2i−2i2i2i-22-20000000000−2i2i1-1ii−i−i0000000000000000000000
χ6244-4-4-2-2-44-222-22200001−4i4i-11-122i2i−2i−2i-22-200000000002i−2i1-1−i−iii0000000000000000000000
χ634-44-44-200-4-4224-24i−4i4i−4i-200-22200000000000000−2i2i−2i2i000000000000000000000000000000
χ644-44-44-200-4-4224-2−4i4i−4i4i-200-222000000000000002i−2i2i−2i000000000000000000000000000000
χ654-44-4-240022-4-4-240000-200-2220000000000−2i22i2−2i22i20000000000000000000000i2−i2i2−i200000000
χ664-44-4-240022-4-4-240000-200-22200000000002i2−2i22i2−2i20000000000000000000000−i2i2−i2i200000000
χ674-4-444-200-44-22-424i−4i−4i4i-20022-200000000000000−2i2i2i−2i000000000000000000000000000000
χ684-4-444-200-44-22-42−4i4i4i−4i-20022-2000000000000002i−2i−2i2i000000000000000000000000000000
χ694-4-44-24002-24-42-40000-20022-20000000000−2i22i22i2−2i20000000000000000000000i2−i2−i2i200000000
χ704-4-44-24002-24-42-40000-20022-200000000002i2−2i2−2i22i20000000000000000000000−i2i2i2−i200000000
χ718-88-8-4-4004444-4-400002002-2-2000000000000000000000000000000000000000000000000
χ728-8-88-4-4004-4-44440000200-2-22000000000000000000000000000000000000000000000000

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