Finite Group Databasebeta

← Group #72271760

Character table — Group #72271760

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222222224444444444444888888888121212121616161616161616161616161616161616161616162424242424242424242424243232323232323232324848484848484896
order1222234444666688881212121224242416161616242424224422244468121616242448484848484848484444448816161616666812121224242444816168
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
χ511111111111111111111111111-1-1-1-1111111111-1-111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-111-1-1-1-1111-1-1-1
χ611111111111111111111111111-1-1-1-11111111-1-111-1-1111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111-1-11111-1-11-1-11
χ711111111111111111111111111-1-1-1-1111-1-1-1-111-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1111
χ811111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111-1-111-1-111-111-1
χ9111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-11-1-1-111-1-111-1-1-11
χ10111111111111111111111111-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-11-1111-1-111-1-1-1-1-1-1
χ11111111111111111111111111-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-11-1-1-11111-1-1111-1
χ12111111111111111111111111-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1111111
χ13111111111111111111111111-1-1-1-1-1-111111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-11-1-1-1-11111-111-1
χ14111111111111111111111111-1-1-1-1-1-11111111-1-1-1-111-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-11-11111-1-1-1-1-1111
χ15111111111111111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1111111-1-11111111-11-1-1-1-1-1-1-1-11-1-11
χ16111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-11-1111111111-1-1-1
χ1722222222222222-2-2-2-22222-2-2220000-2-2-222220000002-2200-2-200000000220000-2-200000000000000000-2000
χ1822222222222222-2-2-2-22222-2-2220000-2-2-2-2-2-2-20000002-2200-2-200000000-2-2000022000000000000000002000
χ1922222222222222-2-2-2-22222-2-2-2-20000-2-2-22222000000-22-2002200000000-2-20000-2-2000000000000000002000
χ2022222222222222-2-2-2-22222-2-2-2-20000-2-2-2-2-2-2-2000000-22-20022000000002200002200000000000000000-2000
χ2122222-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-10000222222-12-122-1-1-1-1-1-1-1-1-1-1000000000000-1-1-12-1-1-1-1-100000000
χ2222222-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-10000-2-2-2-2-2-2-12-122-1-1-1-1-1-1-1-1-1-1000000000000111-21111100000000
χ2322222-12222-1-1-1-12222-1-1-1-1-1-122-2-2-2-2-1-1-1000022-2-222-12-1-2-2-1-111111111000000000000-1-11-21-1-11100000000
χ2422222-12222-1-1-1-12222-1-1-1-1-1-122-2-2-2-2-1-1-10000-2-222-2-2-12-1-2-2-1-11111111100000000000011-12-111-1-100000000
χ2522222-12222-1-1-1-12222-1-1-1-1-1-1-2-22222-1-1-1000022-2-2-2-21-21-2-2111111-1-1-1-1000000000000-1-112111-1-100000000
χ2622222-12222-1-1-1-12222-1-1-1-1-1-1-2-22222-1-1-10000-2-222221-21-2-2111111-1-1-1-100000000000011-1-2-1-1-11100000000
χ2722222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-100002222-2-21-212211-1-1-1-11111000000000000-1-1-1-2-1111100000000
χ2822222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-10000-2-2-2-2221-212211-1-1-1-1111100000000000011121-1-1-1-100000000
χ29222-2-222-22-222-2-222-2-2-2-222220000002-2-20000002-200000000000000000002i2i−2i−2i002i2i−2i−2i0020-2000000000000
χ30222-2-222-22-222-2-222-2-2-2-222220000002-2-20000002-20000000000000000000−2i−2i2i2i00−2i−2i2i2i0020-2000000000000
χ31222-2-222-22-222-2-222-2-2-2-222220000002-2-2000000-2200000000000000000002i2i−2i−2i00−2i−2i2i2i00-202000000000000
χ32222-2-222-22-222-2-222-2-2-2-222220000002-2-2000000-220000000000000000000−2i−2i2i2i002i2i−2i−2i00-202000000000000
χ3322-22-22-2-2222-22-22-22-22-22-2-2-2002i2i−2i−2i22-20000000000000000000002i2i−2i−2i002i−2i2i−2i0000000000000002-2000000
χ3422-22-22-2-2222-22-22-22-22-22-2-2-2002i2i−2i−2i22-20000000000000000000002i2i−2i−2i00−2i2i−2i2i000000000000000-22000000
χ3522-22-22-2-2222-22-22-22-22-22-2-2-200−2i−2i2i2i22-2000000000000000000000−2i−2i2i2i002i−2i2i−2i000000000000000-22000000
χ3622-22-22-2-2222-22-22-22-22-22-2-2-200−2i−2i2i2i22-2000000000000000000000−2i−2i2i2i00−2i2i−2i2i0000000000000002-2000000
χ3722-2-2222-2-222-2-2200002-2-22002-22−22−200022-2-200000020-22−20022−2−22−22−22-20000002−22−2000000000000002−20
χ3822-2-2222-2-222-2-2200002-2-22002-22−22−2000-2-22200000020-22−20022−2−22−22−2-22000000−22−2200000000000000−220
χ3922-2-2222-2-222-2-2200002-2-22002-2−22−2200022-2-200000020-2−2200−2−222−22−222-2000000−22−2200000000000000−220
χ4022-2-2222-2-222-2-2200002-2-22002-2−22−22000-2-22200000020-2−2200−2−222−22−22-220000002−22−2000000000000002−20
χ4122-2-2222-2-222-2-2200002-2-2200-222−22−200022-2-2000000-202−2200−2−2222−22−2-220000002−22−200000000000000−220
χ4222-2-2222-2-222-2-2200002-2-2200-222−22−2000-2-222000000-202−2200−2−2222−22−22-2000000−22−22000000000000002−20
χ4322-2-2222-2-222-2-2200002-2-2200-22−22−2200022-2-2000000-2022−20022−2−2−22−22-22000000−22−22000000000000002−20
χ4422-2-2222-2-222-2-2200002-2-2200-22−22−22000-2-222000000-2022−20022−2−2−22−222-20000002−22−200000000000000−220
χ4522-2-222-222-22-2-222-2-22-222-2-2-20000002-222-22-200002-2000000000000000002-2-222-20000000002-20000000000
χ4622-2-222-222-22-2-222-2-22-222-2-2-20000002-222-22-20000-2200000000000000000-222-22-2000000000-220000000000
χ4722-2-222-222-22-2-222-2-22-222-2-2-20000002-22-22-2200002-200000000000000000-222-2-220000000002-20000000000
χ4822-2-222-222-22-2-222-2-22-222-2-2-20000002-22-22-220000-22000000000000000002-2-22-22000000000-220000000000
χ4922-2-222-222-22-2-22-222-2-222-222000000-22-22-22-22-20000000000000000000000000-2200002-20000000002-20000
χ5022-2-222-222-22-2-22-222-2-222-222000000-22-22-22-2-220000000000000000000000000-220000-22000000000-220000
χ5122-2-222-222-22-2-22-222-2-222-222000000-22-2-22-222-200000000000000000000000002-200002-2000000000-220000
χ5222-2-222-222-22-2-22-222-2-222-222000000-22-2-22-22-2200000000000000000000000002-20000-220000000002-20000
χ53444444-4-4-4-444440000-4-4-4-4000000000004-4-4400000000000000000000000000000000000000000000000000
χ54444444-4-4-4-444440000-4-4-4-400000000000-444-400000000000000000000000000000000000000000000000000
χ5544444-24444-2-2-2-2-4-4-4-4-2-2-2-2224400002220000000000-2-4-200220000000000000000000000000000000000000
χ5644444-24444-2-2-2-2-4-4-4-4-2-2-2-222-4-40000222000000000024200-2-20000000000000000000000000000000000000
χ57444-4-444-44-444-4-4-4-444-4-444-4-4000000-444000000000000000000000000000000000000000000000000000000
χ58444-4-44-44-4444-4-4000044-4-40000−2i22i22i2−2i2000000000000000000000000−2i22i22i2−2i200000000000000000000000000000
χ59444-4-44-44-4444-4-4000044-4-400002i2−2i2−2i22i20000000000000000000000002i2−2i2−2i22i200000000000000000000000000000
χ60444-4-4-24-44-4-2-22244-4-422-2-2-2-2000000-2220000004-40000000000000000000000000000000-202000000000000
χ61444-4-4-24-44-4-2-22244-4-422-2-2-2-2000000-222000000-44000000000000000000000000000000020-2000000000000
χ62444-4-4-24-44-4-2-222-4-44422-2-2220000002-2-200000000000000000000000000000000000000000000−2i32i300000000
χ63444-4-4-24-44-4-2-222-4-44422-2-2220000002-2-2000000000000000000000000000000000000000000002i3−2i300000000
χ64444-4-4-2-44-44-2-2220000-2-2220000−2i22i22i2−2i200000000000000000023−23i6−i6i6−i6i2−i2−i2i200000000000000000000000000000
χ65444-4-4-2-44-44-2-2220000-2-2220000−2i22i22i2−2i2000000000000000000−2323−i6i6−i6i6i2−i2−i2i200000000000000000000000000000
χ66444-4-4-2-44-44-2-2220000-2-22200002i2−2i2−2i22i200000000000000000023−23−i6i6−i6i6−i2i2i2−i200000000000000000000000000000
χ67444-4-4-2-44-44-2-2220000-2-22200002i2−2i2−2i22i2000000000000000000−2323i6−i6i6−i6−i2i2i2−i200000000000000000000000000000
χ6844-44-4444-4-44-44-40000-44-4400000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ6944-44-4444-4-44-44-40000-44-44000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ7044-44-44-4-4444-44-4-44-444-44-444000000-4-44000000000000000000000000000000000000000000000000000000
χ7144-44-4-2-4-444-22-224-44-4-22-2222004i4i−4i−4i-2-22000000000000000000000−2i−2i2i2i00000000000000000000000000000
χ7244-44-4-2-4-444-22-224-44-4-22-222200−4i−4i4i4i-2-220000000000000000000002i2i−2i−2i00000000000000000000000000000
χ7344-44-4-2-4-444-22-22-44-44-22-22-2-200000022-200000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ7444-44-4-2-4-444-22-22-44-44-22-22-2-200000022-2000000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ7544-4-44-24-4-44-222-20000-222-2004-422−2222−220000000000000-20222−2200−2−222−22−2200000000000000000000000000000
χ7644-4-44-24-4-44-222-20000-222-2004-4−2222−22220000000000000-202−22220022−2−22−22−200000000000000000000000000000
χ7744-4-44-24-4-44-222-20000-222-200-4422−2222−22000000000000020-2−22220022−2−2−22−2200000000000000000000000000000
χ7844-4-44-24-4-44-222-20000-222-200-44−2222−2222000000000000020-222−2200−2−2222−22−200000000000000000000000000000
χ7944-4-44-2-444-4-222-24-4-442-2-2222000000-22-2000000004-400000000000000000000000000000000-220000000000
χ8044-4-44-2-444-4-222-24-4-442-2-2222000000-22-200000000-44000000000000000000000000000000002-20000000000
χ8144-4-44-2-444-4-222-2-444-42-2-22-2-20000002-2200004-40000000000000000000000000000000-22000000000000000
χ8244-4-44-2-444-4-222-2-444-42-2-22-2-20000002-220000-4400000000000000000000000000000002-2000000000000000
χ8388888-4-8-8-8-8-4-4-4-40000444400000000000000000000000000000000000000000000000000000000000000000
χ8488-88-8-488-8-8-44-4400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ8516-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000
χ8616-16000-800008000000000004i6−4i6000000000000000000000000000000000000000000000000000000000000000
χ8716-16000-80000800000000000−4i64i6000000000000000000000000000000000000000000000000000000000000000

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