Finite Group Databasebeta

← Group #72271722

Character table — Group #72271722

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222222222244444444448888888888121212121616161616161616161616161616161616161616162424242424242424242424243232323232323232324848484848484896
order1222234444612126668888121212441616161624242424224424444481212161624244848484848484848244444881616161668121212121224242224816168
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1
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
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11
χ51111111111111111111111111-1-1-1-11111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-1111-1-111-1-11
χ61111111111111111111111111-1-1-1-111111111-1-11111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-111-11-1-1-1
χ71111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-111-111-1-111-1
χ81111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-11-1-11-1111
χ911111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111-1111-1-1-1-11-1-11-1-1-1-1
χ1011111111111111111111111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-11-1-1-11111-111-1-1-1-11
χ1111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-111-11111
χ1211111111111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-1-1-111111-1-11111-1
χ1311111111111111111111111-1-1-1-1-1-11111111111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-11-1-111-1-11111-111-1
χ1411111111111111111111111-1-1-1-1-1-111111111-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-11-111-1-111-1-1-1-1-1111
χ1511111111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-111-1-1-1-1-1-11111111111-1-111111-11-1-111-1-1-1-1-1-11-1-11
χ1611111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-111-1-11111111-1-1-1
χ172222222222222222-2-2-2-2222220000-2-2-2-22222000000-22200-2-200000000220000-2-200000000000000000-2000
χ182222222222222222-2-2-2-2222220000-2-2-2-2-2-2-2-2000000-22200-2-200000000-2-2000022000000000000000002000
χ192222222222222222-2-2-2-2222-2-20000-2-2-2-222220000002-2-2002200000000-2-20000-2-2000000000000000002000
χ202222222222222222-2-2-2-2222-2-20000-2-2-2-2-2-2-2-20000002-2-20022000000002200002200000000000000000-2000
χ2122222-12222-1-1-1-1-1-12222-1-1-1222222-1-1-1-100002222222-1-122-1-1-1-1-1-1-1-1-1-1000000000000-12-1-1-1-1-1-1-100000000
χ2222222-12222-1-1-1-1-1-12222-1-1-1222222-1-1-1-10000-2-2-2-2-2-22-1-122-1-1-1-1-1-1-1-1-1-10000000000001-2111111100000000
χ2322222-12222-1-1-1-1-1-12222-1-1-122-2-2-2-2-1-1-1-1000022-2-2-2-22-1-1-2-2-1-111111111000000000000-12-11111-1-100000000
χ2422222-12222-1-1-1-1-1-12222-1-1-122-2-2-2-2-1-1-1-10000-2-222222-1-1-2-2-1-1111111110000000000001-21-1-1-1-11100000000
χ2522222-12222-1-1-1-1-1-12222-1-1-1-2-22222-1-1-1-100002222-2-2-211-2-211-1-1-1-11111000000000000-1-2-1-1-1111100000000
χ2622222-12222-1-1-1-1-1-12222-1-1-1-2-22222-1-1-1-10000-2-2-2-222-211-2-211-1-1-1-1111100000000000012111-1-1-1-100000000
χ2722222-12222-1-1-1-1-1-12222-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-222-21122111111-1-1-1-1000000000000-1-2-111-1-11100000000
χ2822222-12222-1-1-1-1-1-12222-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-222-2-2-21122111111-1-1-1-1000000000000121-1-111-1-100000000
χ29222-2-22-22-222222-2-222-2-2-22-2002i2i−2i−2i2-22-2000000000000000002i2i−2i−2i0000002i2i−2i−2i000000000000000200-20000
χ30222-2-22-22-222222-2-222-2-2-22-2002i2i−2i−2i2-22-2000000000000000002i2i−2i−2i000000−2i−2i2i2i000000000000000-20020000
χ31222-2-22-22-222222-2-222-2-2-22-200−2i−2i2i2i2-22-200000000000000000−2i−2i2i2i0000002i2i−2i−2i000000000000000-20020000
χ32222-2-22-22-222222-2-222-2-2-22-200−2i−2i2i2i2-22-200000000000000000−2i−2i2i2i000000−2i−2i2i2i000000000000000200-20000
χ3322-22-22-2-2222-2-2-22-22-22-222-200000022-2-200002-20000000000000000000002i−2i2i−2i002i2i−2i−2i20-200000000000000
χ3422-22-22-2-2222-2-2-22-22-22-222-200000022-2-200002-2000000000000000000000−2i2i−2i2i00−2i−2i2i2i20-200000000000000
χ3522-22-22-2-2222-2-2-22-22-22-222-200000022-2-20000-220000000000000000000002i−2i2i−2i00−2i−2i2i2i-20200000000000000
χ3622-22-22-2-2222-2-2-22-22-22-222-200000022-2-20000-22000000000000000000000−2i2i−2i2i002i2i−2i−2i-20200000000000000
χ3722-2-2222-2-222-2-2-2-222-2-22-2220000002-2-222-22-2002-200000000000000000002-2-222-200000002-2000000000000
χ3822-2-2222-2-222-2-2-2-222-2-22-2220000002-2-222-22-200-220000000000000000000-222-22-20000000-22000000000000
χ3922-2-2222-2-222-2-2-2-222-2-22-2220000002-2-22-22-22002-20000000000000000000-222-2-2200000002-2000000000000
χ4022-2-2222-2-222-2-2-2-222-2-22-2220000002-2-22-22-2200-2200000000000000000002-2-22-220000000-22000000000000
χ4122-2-2222-2-222-2-2-2-22-222-2-222000000-222-22-22-200002-2000000000000000000000-220000000002-20002-200000
χ4222-2-2222-2-222-2-2-2-22-222-2-222000000-222-22-22-20000-22000000000000000000000-22000000000-22000-2200000
χ4322-2-2222-2-222-2-2-2-22-222-2-222000000-222-2-22-2200002-20000000000000000000002-20000000002-2000-2200000
χ4422-2-2222-2-222-2-2-2-22-222-2-222000000-222-2-22-220000-220000000000000000000002-2000000000-220002-200000
χ4522-2-222-222-2222-2-2200002-2-22-22−22−2000022-2-200000002-22−2002−22−222−2−22-20000002−22−2000000000000002−20
χ4622-2-222-222-2222-2-2200002-2-22-22−22−20000-2-22200000002-22−2002−22−222−2−2-22000000−22−2200000000000000−220
χ4722-2-222-222-2222-2-2200002-2-22-2−22−22000022-2-200000002-2−2200−22−22−2−2222-2000000−22−2200000000000000−220
χ4822-2-222-222-2222-2-2200002-2-22-2−22−220000-2-22200000002-2−2200−22−22−2−222-220000002−22−2000000000000002−20
χ4922-2-222-222-2222-2-2200002-2-2-222−22−2000022-2-20000000-22−22002−22−2−2−222-220000002−22−200000000000000−220
χ5022-2-222-222-2222-2-2200002-2-2-222−22−20000-2-2220000000-22−22002−22−2−2−2222-2000000−22−22000000000000002−20
χ5122-2-222-222-2222-2-2200002-2-2-22−22−22000022-2-20000000-222−200−22−2222−2−2-22000000−22−22000000000000002−20
χ5222-2-222-222-2222-2-2200002-2-2-22−22−220000-2-2220000000-222−200−22−2222−2−22-20000002−22−200000000000000−220
χ53444444-4-4-4-44-4-44440000-4-4-400000000004-4-4400000000000000000000000000000000000000000000000000
χ54444444-4-4-4-44-4-44440000-4-4-40000000000-444-400000000000000000000000000000000000000000000000000
χ5544444-24444-2-2-2-2-2-2-4-4-4-4-2-2-244000022220000000000-4-2-200220000000000000000000000000000000000000
χ5644444-24444-2-2-2-2-2-2-4-4-4-4-2-2-2-4-400002222000000000042200-2-20000000000000000000000000000000000000
χ57444-4-444-44-44-4-44-4-400004-440000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ58444-4-444-44-44-4-44-4-400004-4400000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ59444-4-44-44-444444-4-4-4-444-44-4000000-44-44000000000000000000000000000000000000000000000000000000
χ60444-4-4-2-44-44-2-2-2-22244-4-42-22004i4i−4i−4i-22-2200000000000000000−2i−2i2i2i000000000000000000000000000000000
χ61444-4-4-2-44-44-2-2-2-22244-4-42-2200−4i−4i4i4i-22-22000000000000000002i2i−2i−2i000000000000000000000000000000000
χ62444-4-4-2-44-44-2-2-2-222-4-4442-220000002-22-200000000000000000000023−2323−2300000000000000000000000000000
χ63444-4-4-2-44-44-2-2-2-222-4-4442-220000002-22-2000000000000000000000−2323−232300000000000000000000000000000
χ6444-44-4444-4-4444-44-40000-4-4400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ6544-44-4444-4-4444-44-40000-4-44002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ6644-44-44-4-4444-4-4-44-4-44-4444-4000000-4-444000000000000000000000000000000000000000000000000000000
χ6744-44-4-244-4-4-2-2-22-22000022-200−2i22i22i2−2i20000000000000000000−2i32i3i2−i2−i2i26−6−6600000000000000000000000000000
χ6844-44-4-244-4-4-2-2-22-22000022-200−2i22i22i2−2i200000000000000000002i3−2i3i2−i2−i2i2−666−600000000000000000000000000000
χ6944-44-4-244-4-4-2-2-22-22000022-2002i2−2i2−2i22i20000000000000000000−2i32i3−i2i2i2−i2−666−600000000000000000000000000000
χ7044-44-4-244-4-4-2-2-22-22000022-2002i2−2i2−2i22i200000000000000000002i3−2i3−i2i2i2−i26−6−6600000000000000000000000000000
χ7144-44-4-2-4-444-2222-224-44-4-2-22000000-2-22200004-40000000000000000000000000000000-20200000000000000
χ7244-44-4-2-4-444-2222-224-44-4-2-22000000-2-2220000-44000000000000000000000000000000020-200000000000000
χ7344-44-4-2-4-444-2222-22-44-44-2-2200000022-2-20000000000000000000000000000000000000000000023−2300000000
χ7444-44-4-2-4-444-2222-22-44-44-2-2200000022-2-200000000000000000000000000000000000000000000−232300000000
χ7544-4-44-24-4-44-22222-24-4-442-2-2000000-222-20000004-400000000000000000000000000000000-22000000000000
χ7644-4-44-24-4-44-22222-24-4-442-2-2000000-222-2000000-44000000000000000000000000000000002-2000000000000
χ7744-4-44-24-4-44-22222-2-444-42-2-20000002-2-22000000004-400000000000000000000000000000000-220000000000
χ7844-4-44-24-4-44-22222-2-444-42-2-20000002-2-2200000000-44000000000000000000000000000000002-20000000000
χ7944-4-44-2-444-4-2-2-222-20000-2224-422−2222−22000000000000000-2222−2200−22−22−2−22200000000000000000000000000000
χ8044-4-44-2-444-4-2-2-222-20000-2224-4−2222−2222000000000000000-22−2222002−22−222−2−200000000000000000000000000000
χ8144-4-44-2-444-4-2-2-222-20000-222-4422−2222−220000000000000002-2−222200−22−2222−2−200000000000000000000000000000
χ8244-4-44-2-444-4-2-2-222-20000-222-44−2222−22220000000000000002-222−22002−22−2−2−22200000000000000000000000000000
χ8388888-4-8-8-8-8-444-4-4-400004440000000000000000000000000000000000000000000000000000000000000000
χ84888-8-8-48-88-8-444-4440000-44-40000000000000000000000000000000000000000000000000000000000000000
χ8516-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000
χ8616-16000-80000883−8300000000000000000000000000000000000000000000000000000000000000000000000000
χ8716-16000-800008−838300000000000000000000000000000000000000000000000000000000000000000000000000

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