Finite Group Databasebeta

← Group #11721322

Character table — Group #11721322

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11112222224466666666666612121212121212121212181818181818181818181818363636363636363636363636
order1222223666663366666666663666666666444412121212121212122244666612121212
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ51111-1-11111-1-11111-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1
χ61111-1-11111-1-11111-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111
χ71111-1-11111-1-11111-1-1-1-111111-1-1111-1-1-1-1-1-111-1-1-1-111111-1-1111-1-1-1-111
χ81111-1-11111-1-11111-1-1-1-111111-1-1111-1-1-1-1-1-111-1-1-1-11111-111-1-1-11111-1-1
χ92222222222222-1222222-1-1-12-1-1-1-1-1-1-1-1-1-1000000000000020200-1-100-1-1
χ102222222222222-1222222-1-1-12-1-1-1-1-1-1-1-1-1-10000000000000-20-200110011
χ11222222222222-12-1-1-1-1-1-1222-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ12222222222222-12-1-1-1-1-1-1222-1-122-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ132222-2-22222-2-22-122-2-2-2-2-1-1-12-111-1-1-11111000000000000020-200-1-10011
χ142222-2-22222-2-22-122-2-2-2-2-1-1-12-111-1-1-111110000000000000-202001100-1-1
χ152222-2-22222-2-2-12-1-11111222-1-1-2-2-1-1-1111122-2-2-1-1-1-11111000000000000
χ162222-2-22222-2-2-12-1-11111222-1-1-2-2-1-1-11111-2-2221111-1-1-1-1000000000000
χ1722-2-20022-2-200222-200002-2-2-22002-2-20000002i−2i00002i2i−2i−2i000000000000
χ1822-2-20022-2-200222-200002-2-2-22002-2-2000000−2i2i0000−2i−2i2i2i000000000000
χ1922-2-20022-2-200-12-11−i3−i3i3i32-2-21-100-111−i3−i3i3i3002i−2i33−3−3−i−iii000000000000
χ2022-2-20022-2-200-12-11−i3−i3i3i32-2-21-100-111−i3−i3i3i300−2i2i−3−333ii−i−i000000000000
χ2122-2-20022-2-200-12-11i3i3−i3−i32-2-21-100-111i3i3−i3−i3002i−2i−3−333−i−iii000000000000
χ2222-2-20022-2-200-12-11i3i3−i3−i32-2-21-100-111i3i3−i3−i300−2i2i33−3−3ii−i−i000000000000
χ232-22-2002-22-20022-2-20000-22-22200-22-200002-2002-22-20000000000000000
χ242-22-2002-22-20022-2-20000-22-22200-22-20000-2200-22-220000000000000000
χ252-22-2002-22-200-1211−i3i3−i3i3-22-2-1-1001-11−i3i3−i3i32-200-11-11−i3i3−i3i3000000000000
χ262-22-2002-22-200-1211−i3i3−i3i3-22-2-1-1001-11−i3i3−i3i3-22001-11-1i3−i3i3−i3000000000000
χ272-22-2002-22-200-1211i3−i3i3−i3-22-2-1-1001-11i3−i3i3−i32-200-11-11i3−i3i3−i3000000000000
χ282-22-2002-22-200-1211i3−i3i3−i3-22-2-1-1001-11i3−i3i3−i3-22001-11-1−i3i3−i3i3000000000000
χ292-2-222-22-2-222-222-222-2-22-2-22-222-2-2-222-2-22000000000000000000000000
χ302-2-222-22-2-222-22-1-222-2-2211-1-2-1-1111-1-111-1000000000000000000−i3i300−i3i3
χ312-2-222-22-2-222-22-1-222-2-2211-1-2-1-1111-1-111-1000000000000000000i3−i300i3−i3
χ322-2-222-22-2-222-2-121-1-111-1-2-221-12-211-1-111-100003−3−333−3−33000000000000
χ332-2-222-22-2-222-2-121-1-111-1-2-221-12-211-1-111-10000−333−3−333−3000000000000
χ342-2-22-222-2-22-2222-22-222-2-2-22-22-22-2-22-222-2000000000000000000000000
χ352-2-22-222-2-22-222-1-22-222-211-1-2-11-111-11-1-11000000000000000000−i3i300i3−i3
χ362-2-22-222-2-22-222-1-22-222-211-1-2-11-111-11-1-11000000000000000000i3−i300−i3i3
χ372-2-22-222-2-22-22-121-11-1-11-2-221-1-2211-11-1-1100003−3−33−333−3000000000000
χ382-2-22-222-2-22-22-121-11-1-11-2-221-1-2211-11-1-110000−333−33−3−33000000000000
χ39444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111000000000000000000000000
χ404444-4-44444-4-4-2-2-2-22222-2-2-2-2122111-1-1-1-1000000000000000000000000
χ4144-4-40044-4-4004-24-40000-222-4-200-2220000000000000000000000000000
χ4244-4-40044-4-400-2-2-22−2i3−2i32i32i3-22221001-1-1i3i3−i3−i3000000000000000000000000
χ4344-4-40044-4-400-2-2-222i32i3−2i3−2i3-22221001-1-1−i3−i3i3i3000000000000000000000000
χ444-44-4004-44-4004-2-4-400002-224-2002-220000000000000000000000000000
χ454-44-4004-44-400-2-222−2i32i3−2i32i32-22-2100-11-1i3−i3i3−i3000000000000000000000000
χ464-44-4004-44-400-2-2222i3−2i32i3−2i32-22-2100-11-1−i3i3−i3i3000000000000000000000000
χ474-4-444-44-4-444-4-2-22-2-222-222-221-22-1-111-1-11000000000000000000000000
χ484-4-44-444-4-44-44-2-22-22-2-2222-2212-2-1-11-111-1000000000000000000000000
χ49666666-3-3-3-3-3-300000000000000000000000000000000002020-1-100-1-100
χ50666666-3-3-3-3-3-30000000000000000000000000000000000-20-2011001100
χ516666-6-6-3-3-3-333000000000000000000000000000000000020-20-1-1001100
χ526666-6-6-3-3-3-3330000000000000000000000000000000000-20201100-1-100
χ536-6-666-6-333-3-3300000000000000000000000000000000000000−i3i300−i3i300
χ546-6-666-6-333-3-3300000000000000000000000000000000000000i3−i300i3−i300
χ556-6-66-66-333-33-300000000000000000000000000000000000000−i3i300i3−i300
χ566-6-66-66-333-33-300000000000000000000000000000000000000i3−i300−i3i300
χ571212-12-1200-6-666000000000000000000000000000000000000000000000000
χ5812-1212-1200-66-66000000000000000000000000000000000000000000000000

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