Finite Group Databasebeta

← Group #72341570

Character table — Group #72341570

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112266668888121212121212121232323232323232323232323232323232484848484848484848484848484848484848
order1222222222444422224444366666661212121212121212244444444444448888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-11111
χ41111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-1
χ51111-1-1-1-11111-1-11-1-111-1-11111-1-1-1-111111-1-1-1-111-1-11-11-11-111-1-111-1-1
χ61111-1-1-1-11111-1-11-1-111-1-11111-1-1-1-111111-1-1-1-1-1-111-111-1-11-1-111-1-111
χ71111-1-1-1-111-1-1111-1-111-1-11111-1-1-1-11-1-1-1-111111-11-1-11-111-1-1-11111-1-1
χ81111-1-1-1-111-1-1111-1-111-1-11111-1-1-1-11-1-1-1-11111-11-111-1-11-1111-1-1-1-111
χ92222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000220000000000
χ102222222222-2-2-2-222222222-1-1-1-1-1-1-1-111111111000000-2-20000000000
χ112222-2-2-2-22222-2-22-2-222-2-22-1-1-11111-1-1-1-1-111110000002-20000000000
χ122222-2-2-2-222-2-2222-2-222-2-22-1-1-11111-11111-1-1-1-1000000-220000000000
χ132-2-222-22-2-22000022-2-2-22-222-2-222-2-2200000000000000000000000000
χ142-2-222-22-2-22000022-2-2-22-22-111-1-111-1−i3−i3i3i3−i3−i3i3i3000000000000000000
χ152-2-222-22-2-22000022-2-2-22-22-111-1-111-1i3i3−i3−i3i3i3−i3−i3000000000000000000
χ162-2-22-22-22-2200002-22-2-2-2222-2-2-2-222200000000000000000000000000
χ172-2-22-22-22-2200002-22-2-2-222-11111-1-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000
χ182-2-22-22-22-2200002-22-2-2-222-11111-1-1-1i3i3−i3−i3−i3−i3i3i3000000000000000000
χ1933333333333333-1-1-1-1-1-1-1-10000000000000000111111-1-111-1-1-1-1-1-1-1-1
χ2033333333333333-1-1-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1-111111111
χ213333333333-3-3-3-3-1-1-1-1-1-1-1-100000000000000001-1-11-1-111111111-1-1-1-1
χ223333333333-3-3-3-3-1-1-1-1-1-1-1-10000000000000000-111-11111-1-1-1-1-1-11111
χ233333-3-3-3-33333-3-3-111-1-111-1000000000000000011-1-11-1-111-1-1-111-1-111
χ243333-3-3-3-33333-3-3-111-1-111-10000000000000000-1-111-11-11-1111-1-111-1-1
χ253333-3-3-3-333-3-333-111-1-111-100000000000000001-11-1-111-11-111-1-1-1-111
χ263333-3-3-3-333-3-333-111-1-111-10000000000000000-11-111-11-1-11-1-11111-1-1
χ27666666-2-2-2-200002222-2-2-2-200000000000000000220-2-2000000000000
χ28666666-2-2-2-200002222-2-2-2-200000000000000000-2-2022000000000000
χ29666666-2-2-2-20000-2-2-2-22222000000000000000020020000-2-200000000
χ30666666-2-2-2-20000-2-2-2-222220000000000000000-200-200002200000000
χ316666-6-622-2-200002-2-22-222-2000000000000000002-20-22000000000000
χ326666-6-622-2-200002-2-22-222-200000000000000000-2202-2000000000000
χ336666-6-622-2-20000-222-22-2-220000000000000000200-20000-2200000000
χ346666-6-622-2-20000-222-22-2-220000000000000000-200200002-200000000
χ356-6-666-66-6-660000-2-2222-22-20000000000000000000000000000000000
χ366-6-666-6-222-2000022-2-22-22-2000000000000000000000000002i−2i2i−2i0000
χ376-6-666-6-222-2000022-2-22-22-200000000000000000000000000−2i2i−2i2i0000
χ386-6-666-6-222-20000-2-222-22-220000000000000000000000000000002-22-2
χ396-6-666-6-222-20000-2-222-22-22000000000000000000000000000000-22-22
χ406-6-66-662-22-200002-22-222-2-2000000000000000000000000002i−2i−2i2i0000
χ416-6-66-662-22-200002-22-222-2-200000000000000000000000000−2i2i2i−2i0000
χ426-6-66-662-22-20000-22-22-2-2220000000000000000000000000000002-2-22
χ436-6-66-662-22-20000-22-22-2-222000000000000000000000000000000-222-2
χ446-6-66-66-66-660000-22-2222-2-20000000000000000000000000000000000
χ4588-8-8000000004i−4i0000000022-20000-200002i−2i2i−2i000000000000000000
χ4688-8-8000000004i−4i00000000-1-11−i3i3−i3i313−33−3−ii−ii000000000000000000
χ4788-8-8000000004i−4i00000000-1-11i3−i3i3−i31−33−33−ii−ii000000000000000000
χ4888-8-800000000−4i4i0000000022-20000-20000−2i2i−2i2i000000000000000000
χ4988-8-800000000−4i4i00000000-1-11−i3i3−i3i31−33−33i−ii−i000000000000000000
χ5088-8-800000000−4i4i00000000-1-11i3−i3i3−i313−33−3i−ii−i000000000000000000
χ518-88-80000004i−4i00000000002-220000-22i−2i−2i2i0000000000000000000000
χ528-88-80000004i−4i0000000000-11-1−i3i3i3−i31−iii−i3−3−33000000000000000000
χ538-88-80000004i−4i0000000000-11-1i3−i3−i3i31−iii−i−333−3000000000000000000
χ548-88-8000000−4i4i00000000002-220000-2−2i2i2i−2i0000000000000000000000
χ558-88-8000000−4i4i0000000000-11-1−i3i3i3−i31i−i−ii−333−3000000000000000000
χ568-88-8000000−4i4i0000000000-11-1i3−i3−i3i31i−i−ii3−3−33000000000000000000

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