Finite Group Databasebeta

← Group #72270355

Character table — Group #72270355

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222222222244444444448888888888121212121616161616161616161616161616161616161616162424242424242424242424243232323232323232324848484848484896
order12222344446121266688881212124416161616242424242244444488812121616242448484848484848482444448816161616412121212121224242288816164
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-11-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1
χ3111111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11
χ51111111111111111111111111-1-1-1-11111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1
χ61111111111111111111111111-1-1-1-111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-111-1-1111-1-11
χ71111111111111111111111111-1-1-1-11111-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-111111
χ81111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-11111-1-1-111-1
χ911111111111111111111111-1-111111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-111-1-111-1-1-111-1-1-1
χ1011111111111111111111111-1-1111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-1-1-1-11
χ1111111111111111111111111-1-111111111-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1111
χ1211111111111111111111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111-1-111-1-1-1-111111-1
χ1311111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1-1111
χ1411111111111111111111111-1-1-1-1-1-111111111-1-111-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111-11111-1
χ1511111111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111111111-1-1-1-111111-1-1-1
χ1611111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-11111-1-11-1-1-1-11
χ172222222222222222-2-2-2-2222220000-2-2-2-222220000-2002200-2-200000000220000-2-2000000000000000-200000
χ182222222222222222-2-2-2-2222220000-2-2-2-2-2-2-2-20000-2002200-2-200000000-2-2000022000000000000000200000
χ192222222222222222-2-2-2-2222-2-20000-2-2-2-222220000200-2-2002200000000-2-20000-2-2000000000000000200000
χ202222222222222222-2-2-2-2222-2-20000-2-2-2-2-2-2-2-20000200-2-200220000000022000022000000000000000-200000
χ2122222-12222-1-1-1-1-1-12222-1-1-1222222-1-1-1-100002222222-1-122-1-1-1-1-1-1-1-1-1-10000000000002-1-1-1-1-1-1-1-100000000
χ2222222-12222-1-1-1-1-1-12222-1-1-1222222-1-1-1-10000-2-2-2-22-2-2-1-122-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222-12222-1-1-1-1-1-12222-1-1-122-2-2-2-2-1-1-1-1000022222-2-2-1-1-2-2-1-111111111000000000000-211-1-1-1-11100000000
χ2422222-12222-1-1-1-1-1-12222-1-1-122-2-2-2-2-1-1-1-10000-2-2-2-2222-1-1-2-2-1-1111111110000000000002-1-11111-1-100000000
χ2522222-12222-1-1-1-1-1-12222-1-1-1-2-22222-1-1-1-1000022-2-2-22211-2-211-1-1-1-11111000000000000-211-1-111-1-100000000
χ2622222-12222-1-1-1-1-1-12222-1-1-1-2-22222-1-1-1-10000-2-222-2-2-211-2-211-1-1-1-111110000000000002-1-111-1-11100000000
χ2722222-12222-1-1-1-1-1-12222-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-2-2-2-21122111111-1-1-1-10000000000002-1-1-1-1111100000000
χ2822222-12222-1-1-1-1-1-12222-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-222-2221122111111-1-1-1-1000000000000-21111-1-1-1-100000000
χ29222-2-222-22-22-2-2-22-2-22-2222-2000000-2-2220000000002i−2i00000000000000002i2i−2i−2i0022-2-200000002i−2i00000000
χ30222-2-222-22-22-2-2-22-2-22-2222-2000000-2-2220000000002i−2i0000000000000000−2i−2i2i2i00-2-22200000002i−2i00000000
χ31222-2-222-22-22-2-2-22-2-22-2222-2000000-2-222000000000−2i2i00000000000000002i2i−2i−2i00-2-2220000000−2i2i00000000
χ32222-2-222-22-22-2-2-22-2-22-2222-2000000-2-222000000000−2i2i0000000000000000−2i−2i2i2i0022-2-20000000−2i2i00000000
χ3322-22-22-222-22222-2-2-2-222-22-20022-2-22-22-20000000000000000022-2-20000002i−2i2i−2i0000000000000000002i−2i000
χ3422-22-22-222-22222-2-2-2-222-22-20022-2-22-22-20000000000000000022-2-2000000−2i2i−2i2i000000000000000000−2i2i000
χ3522-22-22-222-22222-2-2-2-222-22-200-2-2222-22-200000000000000000-2-2220000002i−2i2i−2i000000000000000000−2i2i000
χ3622-22-22-222-22222-2-2-2-222-22-200-2-2222-22-200000000000000000-2-222000000−2i2i−2i2i0000000000000000002i−2i000
χ3722-2-22222-2-2222-2-2200002-2-22-2−i2i2−i2i2000022-2-200000002-2−i2i200−i2i2−i2i2−i2−i2i2i22-2000000−i2i2−i2i200000000000000−i2i20
χ3822-2-22222-2-2222-2-2200002-2-22-2−i2i2−i2i20000-2-22200000002-2−i2i200−i2i2−i2i2−i2−i2i2i2-22000000i2−i2i2−i200000000000000i2−i20
χ3922-2-22222-2-2222-2-2200002-2-22-2i2−i2i2−i2000022-2-200000002-2i2−i200i2−i2i2−i2i2i2−i2−i22-2000000i2−i2i2−i200000000000000i2−i20
χ4022-2-22222-2-2222-2-2200002-2-22-2i2−i2i2−i20000-2-22200000002-2i2−i200i2−i2i2−i2i2i2−i2−i2-22000000−i2i2−i2i200000000000000−i2i20
χ4122-2-22222-2-2222-2-2200002-2-2-22−i2i2−i2i2000022-2-20000000-22i2−i200−i2i2−i2i2i2i2−i2−i2-22000000−i2i2−i2i200000000000000i2−i20
χ4222-2-22222-2-2222-2-2200002-2-2-22−i2i2−i2i20000-2-2220000000-22i2−i200−i2i2−i2i2i2i2−i2−i22-2000000i2−i2i2−i200000000000000−i2i20
χ4322-2-22222-2-2222-2-2200002-2-2-22i2−i2i2−i2000022-2-20000000-22−i2i200i2−i2i2−i2−i2−i2i2i2-22000000i2−i2i2−i200000000000000−i2i20
χ4422-2-22222-2-2222-2-2200002-2-2-22i2−i2i2−i20000-2-2220000000-22−i2i200i2−i2i2−i2−i2−i2i2i22-2000000−i2i2−i2i200000000000000i2−i20
χ4522-2-222-2-2222-2-2-2-222-2-22-222000000-222-22-22-22-20000000000000000000002-2-222-200000002-2000000000000
χ4622-2-222-2-2222-2-2-2-222-2-22-222000000-222-22-22-2-22000000000000000000000-222-22-20000000-22000000000000
χ4722-2-222-2-2222-2-2-2-222-2-22-222000000-222-2-22-222-2000000000000000000000-222-2-2200000002-2000000000000
χ4822-2-222-2-2222-2-2-2-222-2-22-222000000-222-2-22-22-220000000000000000000002-2-22-220000000-22000000000000
χ4922-2-222-2-2222-2-2-2-22-222-2-2220000002-2-222-22-2002-200000000000000000000000-220000000002-2002-2000000
χ5022-2-222-2-2222-2-2-2-22-222-2-2220000002-2-222-22-200-2200000000000000000000000-22000000000-2200-22000000
χ5122-2-222-2-2222-2-2-2-22-222-2-2220000002-2-22-22-22002-2000000000000000000000002-20000000002-200-22000000
χ5222-2-222-2-2222-2-2-2-22-222-2-2220000002-2-22-22-2200-22000000000000000000000002-2000000000-22002-2000000
χ53444444-4-4-4-44-4-44440000-4-4-400000000004-4-4400000000000000000000000000000000000000000000000000
χ54444444-4-4-4-44-4-44440000-4-4-40000000000-444-400000000000000000000000000000000000000000000000000
χ5544444-24444-2-2-2-2-2-2-4-4-4-4-2-2-2440000222200000000-400-2-200220000000000000000000000000000000000000
χ5644444-24444-2-2-2-2-2-2-4-4-4-4-2-2-2-4-400002222000000004002200-2-20000000000000000000000000000000000000
χ57444-4-444-44-44-4-4-44-44-44-444-400000044-4-4000000000000000000000000000000000000000000000000000000
χ58444-4-44-44-44444-44-40000-4-4400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ59444-4-44-44-44444-44-40000-4-44002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ60444-4-4-24-44-4-2222-224-44-4-2-22000000-2-22200000000000000000000000000000000000000−2i32i300000000000000
χ61444-4-4-24-44-4-2222-224-44-4-2-22000000-2-222000000000000000000000000000000000000002i3−2i300000000000000
χ62444-4-4-24-44-4-2222-22-44-44-2-2200000022-2-20000000004i−4i000000000000000000000000000000000−2i2i00000000
χ63444-4-4-24-44-4-2222-22-44-44-2-2200000022-2-2000000000−4i4i0000000000000000000000000000000002i−2i00000000
χ64444-4-4-2-44-44-2-2-22-22000022-200−2i22i22i2−2i20000000000000000000−2i32i3i2−i2−i2i26−66−600000000000000000000000000000
χ65444-4-4-2-44-44-2-2-22-22000022-200−2i22i22i2−2i200000000000000000002i3−2i3i2−i2−i2i2−66−6600000000000000000000000000000
χ66444-4-4-2-44-44-2-2-22-22000022-2002i2−2i2−2i22i20000000000000000000−2i32i3−i2i2i2−i2−66−6600000000000000000000000000000
χ67444-4-4-2-44-44-2-2-22-22000022-2002i2−2i2−2i22i200000000000000000002i3−2i3−i2i2i2−i26−66−600000000000000000000000000000
χ6844-44-444-4-444-4-44-4-400004-440000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ6944-44-444-4-444-4-44-4-400004-4400000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ7044-44-44-444-44444-4-444-4-4-44-4000000-44-44000000000000000000000000000000000000000000000000000000
χ7144-44-4-2-444-4-2-2-2-22244-4-42-220000002-22-2000000000000000000000−2i32i32i3−2i300000000000000000000000000000
χ7244-44-4-2-444-4-2-2-2-22244-4-42-220000002-22-20000000000000000000002i3−2i3−2i32i300000000000000000000000000000
χ7344-44-4-2-444-4-2-2-2-222-4-4442-220044-4-4-22-2200000000000000000-2-222000000000000000000000000000000000
χ7444-44-4-2-444-4-2-2-2-222-4-4442-2200-4-444-22-220000000000000000022-2-2000000000000000000000000000000000
χ7544-4-44-244-4-4-2-2-222-20000-2224-4−2i22i2−2i22i2000000000000000-22−2i22i200i2−i2i2−i2i2i2−i2−i200000000000000000000000000000
χ7644-4-44-244-4-4-2-2-222-20000-2224-42i2−2i22i2−2i2000000000000000-222i2−2i200−i2i2−i2i2−i2−i2i2i200000000000000000000000000000
χ7744-4-44-244-4-4-2-2-222-20000-222-44−2i22i2−2i22i20000000000000002-22i2−2i200i2−i2i2−i2−i2−i2i2i200000000000000000000000000000
χ7844-4-44-244-4-4-2-2-222-20000-222-442i2−2i22i2−2i20000000000000002-2−2i22i200−i2i2−i2i2i2i2−i2−i200000000000000000000000000000
χ7944-4-44-2-4-444-22222-24-4-442-2-20000002-2-2200004-40000000000000000000000000000000000-22000000000000
χ8044-4-44-2-4-444-22222-24-4-442-2-20000002-2-220000-4400000000000000000000000000000000002-2000000000000
χ8144-4-44-2-4-444-22222-2-444-42-2-2000000-222-20000004-40000000000000000000000000000000000-220000000000
χ8244-4-44-2-4-444-22222-2-444-42-2-2000000-222-2000000-4400000000000000000000000000000000002-20000000000
χ8388888-4-8-8-8-8-444-4-4-400004440000000000000000000000000000000000000000000000000000000000000000
χ8488-88-8-48-8-88-444-4440000-44-40000000000000000000000000000000000000000000000000000000000000000
χ8516-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000
χ8616-16000-80000883−8300000000000000000000000000000000000000000000000000000000000000000000000000
χ8716-16000-800008−838300000000000000000000000000000000000000000000000000000000000000000000000000

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