Finite Group Databasebeta

← Group #72231678

Character table — Group #72231678

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222244444444444888888888888888161616161616161616161616162424242432323232323232323232323248484848484896969696
order12222362222222266624466666666661212244466121212121212122222444412121212121212122444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ5111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-111
χ7111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1
χ92222222222222-2-2222-2-2-22222-2-222-2-2-2-2000000-2000000222200000000000000-2-2000000
χ102222222222222-2-2222-2-2-22222-2-222-2-2-2-2000000-2000000-2-2-2-20000000000000022000000
χ11222222222-2-2-2-2222222-2-222-2-222-2-222-2-2000000-20000000000000000000000000000002-2
χ12222222222-2-2-2-2222222-2-222-2-222-2-222-2-2000000-2000000000000000000000000000000-22
χ13222222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-22200000020000000000002i−2i00002i2i−2i−2i0000000000
χ14222222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-2220000002000000000000−2i2i0000−2i−2i2i2i0000000000
χ152222222-2-222-2-222222-22-2-2-2-2-22222-2-2-2-2000000200000000000000000000002200-2-20000
χ162222222-2-222-2-222222-22-2-2-2-2-22222-2-2-2-200000020000000000000000000000-2-200220000
χ172222222-2-222-2-2-2-22222-22-2-2-2-2-2-2222222000000-200000000002-20022-2-200000000000000
χ182222222-2-222-2-2-2-22222-22-2-2-2-2-2-2222222000000-20000000000-2200-2-22200000000000000
χ192222222-2-2-2-22222222-2-22-2-22222-2-2-2-22222-2-222-222-2-2-2-200000000000000000000000000
χ202222222-2-2-2-22222222-2-22-2-22222-2-2-2-222-2-222-2-2-2-2-2222200000000000000000000000000
χ212222222-2-2-2-222-2-222222-2-2-222-2-2-2-222-2-2000000200000000000000000000000000002-200
χ222222222-2-2-2-222-2-222222-2-2-222-2-2-2-222-2-200000020000000000000000000000000000-2200
χ2322222-1-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-10000000000
χ2422222-1-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-10000-2-2-2-2111111110000000000
χ2522222-1-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-1111111000022-2-2-1-1-1-111110000000000
χ2622222-1-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-11111110000-2-2221111-1-1-1-10000000000
χ2722222-1-122-2-2-2-2-2-2-1-1-1-222-1-111111111-1-10000−i3i3-1−i3i3−i3−i3i3i30000002i−2i3−33−3−i−iii0000000000
χ2822222-1-122-2-2-2-2-2-2-1-1-1-222-1-111111111-1-10000−i3i3-1−i3i3−i3−i3i3i3000000−2i2i−33−33ii−i−i0000000000
χ2922222-1-122-2-2-2-2-2-2-1-1-1-222-1-111111111-1-10000i3−i3-1i3−i3i3i3−i3−i30000002i−2i−33−33−i−iii0000000000
χ3022222-1-122-2-2-2-2-2-2-1-1-1-222-1-111111111-1-10000i3−i3-1i3−i3i3i3−i3−i3000000−2i2i3−33−3ii−i−i0000000000
χ3122222-1-1-2-222-2-2-2-2-1-1-12-22111111-1-1-1-1-1-10000−i3i31−i3i3i3i3−i3−i300002-200-1-111−i3i3−i3i30000000000
χ3222222-1-1-2-222-2-2-2-2-1-1-12-22111111-1-1-1-1-1-10000−i3i31−i3i3i3i3−i3−i30000-220011-1-1i3−i3i3−i30000000000
χ3322222-1-1-2-222-2-2-2-2-1-1-12-22111111-1-1-1-1-1-10000i3−i31i3−i3−i3−i3i3i300002-200-1-111i3−i3i3−i30000000000
χ3422222-1-1-2-222-2-2-2-2-1-1-12-22111111-1-1-1-1-1-10000i3−i31i3−i3−i3−i3i3i30000-220011-1-1−i3i3−i3i30000000000
χ3522222-1-1-2-2-2-22222-1-1-1-2-2211-1-1-1-11111-1-122-2-2-1-11-1-11111000000003−3−333−3−330000000000
χ3622222-1-1-2-2-2-22222-1-1-1-2-2211-1-1-1-11111-1-122-2-2-1-11-1-1111100000000−333−3−333−30000000000
χ3722222-1-1-2-2-2-22222-1-1-1-2-2211-1-1-1-11111-1-1-2-22211111-1-1-1-1000000003−3−33−333−30000000000
χ3822222-1-1-2-2-2-22222-1-1-1-2-2211-1-1-1-11111-1-1-2-22211111-1-1-1-100000000−333−33−3−330000000000
χ3944444-2-2444444-4-4-2-2-2-4-4-4-2-2-2-222-2-22222000000200000000000000000000000000000000
χ4044444-2-244-4-4-4-444-2-2-24-4-4-2-222-2-222-2-222000000200000000000000000000000000000000
χ4144444-2-2-4-444-4-444-2-2-2-44-42222-2-2-2-22222000000-200000000000000000000000000000000
χ4244444-2-2-4-4-4-444-4-4-2-2-244-422-2-22222-2-222000000-200000000000000000000000000000000
χ43444-4-444004-40000-4-440000000004-400002-22-2220-2-22-22-200000000000000000000000000
χ44444-4-444004-40000-4-440000000004-40000-22-22-2-2022-22-2200000000000000000000000000
χ45444-4-44400-440000-4-44000000000-4400002-2-22220-2-2-22-2200000000000000000000000000
χ46444-4-44400-440000-4-44000000000-440000-222-2-2-20222-22-200000000000000000000000000
χ47444-4-4-2-2004-4000022-2000000000-22−2i32i3−2i32i32-22-2−1−i3−1+i301+i31−i3−1+i31−i3−1−i31+i300000000000000000000000000
χ48444-4-4-2-2004-4000022-2000000000-22−2i32i3−2i32i3-22-221+i31−i30−1−i3−1+i31−i3−1+i31+i3−1−i300000000000000000000000000
χ49444-4-4-2-2004-4000022-2000000000-222i3−2i32i3−2i32-22-2−1+i3−1−i301−i31+i3−1−i31+i3−1+i31−i300000000000000000000000000
χ50444-4-4-2-2004-4000022-2000000000-222i3−2i32i3−2i3-22-221−i31+i30−1+i3−1−i31+i3−1−i31−i3−1+i300000000000000000000000000
χ51444-4-4-2-200-44000022-20000000002-2−2i32i32i3−2i32-2-22−1+i3−1−i301−i31+i31+i3−1−i31−i3−1+i300000000000000000000000000
χ52444-4-4-2-200-44000022-20000000002-2−2i32i32i3−2i3-222-21−i31+i30−1+i3−1−i3−1−i31+i3−1+i31−i300000000000000000000000000
χ53444-4-4-2-200-44000022-20000000002-22i3−2i3−2i32i32-2-22−1−i3−1+i301+i31−i31−i3−1+i31+i3−1−i300000000000000000000000000
χ54444-4-4-2-200-44000022-20000000002-22i3−2i3−2i32i3-222-21+i31−i30−1−i3−1+i3−1+i31−i3−1−i31+i300000000000000000000000000
χ5544-44-4440000004-44-4-400000004-4000000000000000000022-2-2000000000000002-2000000
χ5644-44-4440000004-44-4-400000004-40000000000000000000-2-22200000000000000-22000000
χ5744-44-444000000-444-4-40000000-44000000000000000000022-2-200000000000000-22000000
χ5844-44-444000000-444-4-40000000-440000000000000000000-2-222000000000000002-2000000
χ5944-4-444400004-400-44-4000004-400000000000000000000000000000000000002-2002-20000
χ6044-4-444400004-400-44-4000004-40000000000000000000000000000000000000-2200-220000
χ6144-4-44440000-4400-44-400000-4400000000000000000000000000000000000002-200-220000
χ6244-4-44440000-4400-44-400000-440000000000000000000000000000000000000-22002-20000
χ6388-88-8-4-40000008-8-4440000000-44000000000000000000000000000000000000000000000
χ6488-88-8-4-4000000-88-44400000004-4000000000000000000000000000000000000000000000
χ6588-8-88-4-400008-8004-4400000-4400000000000000000000000000000000000000000000000
χ6688-8-88-4-40000-88004-44000004-400000000000000000000000000000000000000000000000
χ678-80008-84-40000000000004-400000000000000000000000004-40000000000000000000000
χ688-80008-84-40000000000004-40000000000000000000000000-440000000000000000000000
χ698-80008-8-44000000000000-44000000000000000000000004-4000000000000000000000000
χ708-80008-8-44000000000000-4400000000000000000000000-44000000000000000000000000
χ7116-16000-888-8000000000000-440000000000000000000000000000000000000000000000000
χ7216-16000-88-880000000000004-40000000000000000000000000000000000000000000000000

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