Finite Group Databasebeta

← Group #11721793

Character table — Group #11721793

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61
size111111222444444444666666661212121212121212121212121818181818182424242424242424363636363636363636
order12336641212226666824243333666612121212242424242424242424661212666666662466812122424
χ11111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1
χ31111111111-111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11-111-1-1-1-1-1
χ41111111111-111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111111
χ5111111111-11-1-111-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-11-1-1-111-1-1
χ6111111111-11-1-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1-111
χ7111111111-1-1-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111
χ8111111111-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1
χ92222222222222222222-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10000002-1-1-12-1-1-1000000000
χ10222222222222222222-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1000000-12-1-1-12-1-1000000000
χ11222222222222222222-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1000000-1-12-1-1-12-1000000000
χ12222222222222222222-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122000000-1-1-12-1-1-12000000000
χ132222222222-222-2-2-2-2-22-1-1-12-1-1-12-1-1-1-2-21111110000002-1-1-1-2111000000000
χ142222222222-222-2-2-2-2-2-12-1-1-12-1-1-12-1-111-2-21111000000-12-1-11-211000000000
χ152222222222-222-2-2-2-2-2-1-12-1-1-12-1-1-12-11111-2-211000000-1-12-111-21000000000
χ162222222222-222-2-2-2-2-2-1-1-12-1-1-12-1-1-12111111-2-2000000-1-1-12111-2000000000
χ17222222222-22-2-222-2-2-22-1-1-12-1-1-12-1-1-1-2-2111111000000-21112-1-1-1000000000
χ18222222222-22-2-222-2-2-2-12-1-1-12-1-1-12-1-111-2-211110000001-211-12-1-1000000000
χ19222222222-22-2-222-2-2-2-1-12-1-1-12-1-1-12-11111-2-21100000011-21-1-12-1000000000
χ20222222222-22-2-222-2-2-2-1-1-12-1-1-12-1-1-12111111-2-2000000111-2-1-1-12000000000
χ21222222222-2-2-2-2-2-22222-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1000000-2111-2111000000000
χ22222222222-2-2-2-2-2-2222-12-1-1-12-1-1-12-1-1-1-122-1-1-1-10000001-2111-211000000000
χ23222222222-2-2-2-2-2-2222-1-12-1-1-12-1-1-12-1-1-1-1-122-1-100000011-2111-21000000000
χ24222222222-2-2-2-2-2-2222-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122000000111-2111-2000000000
χ25222222-2-2-200000000022222222-2-2-2-2000000002-222-2-200000000000000000
χ26222222-2-2-200000000022222222-2-2-2-200000000-22-2-22200000000000000000
χ2733−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i320000000000000000000011−1−i32−1+i32−1−i32−1+i320000000011−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32
χ2833−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3200000000000000000000-1-11+i321−i321+i321−i3200000000-1-11+i321−i32-11+i321−i321+i321−i32
χ2933−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323-3−3−3i32−3+3i323+3i323−3i32-33+3i323−3i320000000000000000000011−1−i32−1+i32−1−i32−1+i32000000001-1−1−i32−1+i32-11+i321−i321+i321−i32
χ3033−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323-3−3−3i32−3+3i323+3i323−3i32-33+3i323−3i3200000000000000000000-1-11+i321−i321+i321−i3200000000-111+i321−i321−1−i32−1+i32−1−i32−1+i32
χ3133−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-333+3i323−3i32−3−3i32−3+3i32-33+3i323−3i320000000000000000000011−1−i32−1+i32−1−i32−1+i3200000000-111+i321−i32-1−1−i32−1+i321+i321−i32
χ3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-333+3i323−3i32−3−3i32−3+3i32-33+3i323−3i3200000000000000000000-1-11+i321−i321+i321−i32000000001-1−1−i32−1+i3211+i321−i32−1−i32−1+i32
χ3333−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i323−3−3i32−3+3i320000000000000000000011−1−i32−1+i32−1−i32−1+i3200000000-1-11+i321−i3211+i321−i32−1−i32−1+i32
χ3433−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i323−3−3i32−3+3i3200000000000000000000-1-11+i321−i321+i321−i320000000011−1−i32−1+i32-1−1−i32−1+i321+i321−i32
χ3533−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i320000000000000000000011−1+i32−1−i32−1+i32−1−i320000000011−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32
χ3633−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3200000000000000000000-1-11−i321+i321−i321+i3200000000-1-11−i321+i32-11−i321+i321−i321+i32
χ3733−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323-3−3+3i32−3−3i323−3i323+3i32-33−3i323+3i320000000000000000000011−1+i32−1−i32−1+i32−1−i32000000001-1−1+i32−1−i32-11−i321+i321−i321+i32
χ3833−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323-3−3+3i32−3−3i323−3i323+3i32-33−3i323+3i3200000000000000000000-1-11−i321+i321−i321+i3200000000-111−i321+i321−1+i32−1−i32−1+i32−1−i32
χ3933−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-333−3i323+3i32−3+3i32−3−3i32-33−3i323+3i320000000000000000000011−1+i32−1−i32−1+i32−1−i3200000000-111−i321+i32-1−1+i32−1−i321−i321+i32
χ4033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-333−3i323+3i32−3+3i32−3−3i32-33−3i323+3i3200000000000000000000-1-11−i321+i321−i321+i32000000001-1−1+i32−1−i3211−i321+i32−1+i32−1−i32
χ4133−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i323−3+3i32−3−3i320000000000000000000011−1+i32−1−i32−1+i32−1−i3200000000-1-11−i321+i3211−i321+i32−1+i32−1−i32
χ4233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i323−3+3i32−3−3i3200000000000000000000-1-11−i321+i321−i321+i320000000011−1+i32−1−i32-1−1+i32−1−i321−i321+i32
χ43444444-4-4-40000000004-2-2-24-2-2-2-42220000000000000000000000000000000
χ44444444-4-4-4000000000-24-2-2-24-2-22-4220000000000000000000000000000000
χ45444444-4-4-4000000000-2-24-2-2-24-222-420000000000000000000000000000000
χ46444444-4-4-4000000000-2-2-24-2-2-24222-40000000000000000000000000000000
χ474-444-4-40000000000004444-4-4-4-400000000000000000000000000000000000
χ484-444-4-40000000000004-2-2-2-4222000000i6−i6i6−i6i6−i600000000000000000000000
χ494-444-4-40000000000004-2-2-2-4222000000−i6i6−i6i6−i6i600000000000000000000000
χ504-444-4-4000000000000-24-2-22-4220000i6−i600i6−i6−i6i600000000000000000000000
χ514-444-4-4000000000000-24-2-22-4220000−i6i600−i6i6i6−i600000000000000000000000
χ524-444-4-4000000000000-2-24-222-420000i6−i6−i6i600i6−i600000000000000000000000
χ534-444-4-4000000000000-2-24-222-420000−i6i6i6−i600−i6i600000000000000000000000
χ544-444-4-4000000000000-2-2-24222-40000i6−i6i6−i6−i6i60000000000000000000000000
χ554-444-4-4000000000000-2-2-24222-40000−i6i6−i6i6i6−i60000000000000000000000000
χ5666−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i3000000000000000000000000000002-2−1−i3−1+i31+i31−i300000000000000000
χ5766−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300000000000000000000000000000-221+i31−i3−1−i3−1+i300000000000000000
χ5866−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i3000000000000000000000000000002-2−1+i3−1−i31−i31+i300000000000000000
χ5966−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i300000000000000000000000000000-221−i31+i3−1+i3−1−i300000000000000000
χ6012-12−6−6i3−6+6i36+6i36−6i30000000000000000000000000000000000000000000000000000000
χ6112-12−6+6i3−6−6i36−6i36+6i30000000000000000000000000000000000000000000000000000000

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