Finite Group Databasebeta

← Group #72271540

Character table — Group #72271540

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222222244444444444448888888888888888812121212161616161616161616161616161616161616161616161616162424242424242424323232323248484848484848484896
order12222344446666888812121212242424444466121216161616242424224424448121212121212121216162424484848484848484844881616161668122424222444816168
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111-1-111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111-1-1-1
χ41111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1111
χ511111111111111111111111111-1-1-1-1111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111-1
χ611111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11
χ711111111111111111111111111-1-1-1-11111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-11-1-11
χ811111111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-111-1
χ9111111111111111111111111-1-11111-1-1-1-11111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-11-1-1-1-11111-1-1-1-1
χ10111111111111111111111111-1-11111-1-1-1-11111111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-11-1-111-1-1-1-11111
χ11111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-11-111-1-1-1-111-1111
χ12111111111111111111111111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11111-11-1111111-1-11-1-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-11-11111-1-1-1-1-1-1-11
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11-111-1-11111111-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-11-11-1-11111-1-1-111-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-11111-1-1-1-111-1-111111-11-1-1-1-1-1-1111-1-11
χ1722222222222222-2-2-2-22222-2-222000022220000-2-2-222220000-20000000000-2-20000000022-2-2000000000000000-2000
χ1822222222222222-2-2-2-22222-2-222000022220000-2-2-2-2-2-2-20000-20000000000-2-200000000-2-2220000000000000002000
χ1922222222222222-2-2-2-22222-2-2-2-20000-2-2-2-20000-2-2-222220000200000000002200000000-2-2-2-20000000000000002000
χ2022222222222222-2-2-2-22222-2-2-2-20000-2-2-2-20000-2-2-2-2-2-2-200002000000000022000000002222000000000000000-2000
χ2122222-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-12222-1-1-1000022222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000-12-1-1-10000000000
χ2222222-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-10000-2-2222-1-1-1-1-1-1-1-1-2-2-1-111111111000000001-21110000000000
χ2322222-12222-1-1-1-12222-1-1-1-1-1-122-2-2-2-2-1-1-1-12222-1-1-10000-2-2-2-221111111122-1-1-1-1-1-1-1-1-1-1000000001-21110000000000
χ2422222-12222-1-1-1-12222-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-1-1-1000022-2-2211111111-2-2-1-11111111100000000-12-1-1-10000000000
χ2522222-12222-1-1-1-12222-1-1-1-1-1-1-2-2222211112222-1-1-1000022-2-2-2-1-1-1-11111-2-2111111-1-1-1-100000000-1-2-1110000000000
χ2622222-12222-1-1-1-12222-1-1-1-1-1-1-2-222221111-2-2-2-2-1-1-10000-2-2-2-2-2-1-1-1-111112211-1-1-1-1111100000000121-1-10000000000
χ2722222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-211112222-1-1-10000-2-222-21111-1-1-1-1-2-2111111-1-1-1-100000000121-1-10000000000
χ2822222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-21111-2-2-2-2-1-1-100002222-21111-1-1-1-12211-1-1-1-1111100000000-1-2-1110000000000
χ29222-2-222-22-222-2-22-22-2-2-222-2-2002i2i−2i−2i00002i2i−2i−2i22-200002-20002i2i−2i−2i0000000000002i2i−2i−2i0000000020-2000000000000
χ30222-2-222-22-222-2-22-22-2-2-222-2-2002i2i−2i−2i0000−2i−2i2i2i22-20000-220002i2i−2i−2i000000000000−2i−2i2i2i00000000-202000000000000
χ31222-2-222-22-222-2-22-22-2-2-222-2-200−2i−2i2i2i00002i2i−2i−2i22-20000-22000−2i−2i2i2i0000000000002i2i−2i−2i00000000-202000000000000
χ32222-2-222-22-222-2-22-22-2-2-222-2-200−2i−2i2i2i0000−2i−2i2i2i22-200002-2000−2i−2i2i2i000000000000−2i−2i2i2i0000000020-2000000000000
χ33222-2-2-12-22-2-1-1112-22-211-1-111002i2i−2i−2i−i3i3−i3i32i2i−2i−2i-1-1100002-2000−i−iii33−3−300−i3i333−3−3−i−iii00000000-101−i3i30000000000
χ34222-2-2-12-22-2-1-1112-22-211-1-111002i2i−2i−2i−i3i3−i3i3−2i−2i2i2i-1-110000-22000−i−iii33−3−300−i3i3−3−333ii−i−i0000000010-1i3−i30000000000
χ35222-2-2-12-22-2-1-1112-22-211-1-111002i2i−2i−2ii3−i3i3−i32i2i−2i−2i-1-1100002-2000−i−iii−3−33300i3−i3−3−333−i−iii00000000-101i3−i30000000000
χ36222-2-2-12-22-2-1-1112-22-211-1-111002i2i−2i−2ii3−i3i3−i3−2i−2i2i2i-1-110000-22000−i−iii−3−33300i3−i333−3−3ii−i−i0000000010-1−i3i30000000000
χ37222-2-2-12-22-2-1-1112-22-211-1-11100−2i−2i2i2i−i3i3−i3i32i2i−2i−2i-1-110000-22000ii−i−i−3−33300−i3i333−3−3−i−iii0000000010-1i3−i30000000000
χ38222-2-2-12-22-2-1-1112-22-211-1-11100−2i−2i2i2i−i3i3−i3i3−2i−2i2i2i-1-1100002-2000ii−i−i−3−33300−i3i3−3−333ii−i−i00000000-101−i3i30000000000
χ39222-2-2-12-22-2-1-1112-22-211-1-11100−2i−2i2i2ii3−i3i3−i32i2i−2i−2i-1-110000-22000ii−i−i33−3−300i3−i3−3−333−i−iii0000000010-1−i3i30000000000
χ40222-2-2-12-22-2-1-1112-22-211-1-11100−2i−2i2i2ii3−i3i3−i3−2i−2i2i2i-1-1100002-2000ii−i−i33−3−300i3−i333−3−3ii−i−i00000000-101i3−i30000000000
χ4122-22-22-2-2222-22-222-2-22-22-222002i−2i2i−2i000000002-2-20000000002i−2i2i−2i000000000000000000002i2i−2i−2i00000002-2000000
χ4222-22-22-2-2222-22-222-2-22-22-222002i−2i2i−2i000000002-2-20000000002i−2i2i−2i00000000000000000000−2i−2i2i2i0000000-22000000
χ4322-22-22-2-2222-22-222-2-22-22-22200−2i2i−2i2i000000002-2-2000000000−2i2i−2i2i000000000000000000002i2i−2i−2i0000000-22000000
χ4422-22-22-2-2222-22-222-2-22-22-22200−2i2i−2i2i000000002-2-2000000000−2i2i−2i2i00000000000000000000−2i−2i2i2i00000002-2000000
χ4522-2-2222-2-222-2-2200002-2-22002-2000022-2-22−22−200022-2-200000000000002−2002−22−22−22−22-2002−22−20000000000002−20
χ4622-2-2222-2-222-2-2200002-2-22002-2000022-2-22−22−2000-2-22200000000000002−2002−22−22−22−2-2200−22−22000000000000−220
χ4722-2-2222-2-222-2-2200002-2-22002-2000022-2-2−22−2200022-2-20000000000000−2200−22−22−22−222-200−22−22000000000000−220
χ4822-2-2222-2-222-2-2200002-2-22002-2000022-2-2−22−22000-2-2220000000000000−2200−22−22−22−22-22002−22−20000000000002−20
χ4922-2-2222-2-222-2-2200002-2-2200-220000-2-2222−22−200022-2-20000000000000−2200−22−222−22−2-22002−22−2000000000000−220
χ5022-2-2222-2-222-2-2200002-2-2200-220000-2-2222−22−2000-2-2220000000000000−2200−22−222−22−22-200−22−220000000000002−20
χ5122-2-2222-2-222-2-2200002-2-2200-220000-2-222−22−2200022-2-200000000000002−2002−22−2−22−22-2200−22−220000000000002−20
χ5222-2-2222-2-222-2-2200002-2-2200-220000-2-222−22−22000-2-22200000000000002−2002−22−2−22−222-2002−22−2000000000000−220
χ5322-2-222-222-22-2-222-2-22-222-2-2-2002-2-22000000002-222-22-2000002-2-220000000000000000002-200000000000002-20000
χ5422-2-222-222-22-2-222-2-22-222-2-2-2002-2-22000000002-22-22-22000002-2-22000000000000000000-220000000000000-220000
χ5522-2-222-222-22-2-222-2-22-222-2-2-200-222-2000000002-222-22-200000-222-20000000000000000002-20000000000000-220000
χ5622-2-222-222-22-2-222-2-22-222-2-2-200-222-2000000002-22-22-2200000-222-2000000000000000000-2200000000000002-20000
χ5722-2-222-222-22-2-22-222-2-222-22200000000000000-22-22-22-2002-2000002-22-200000000000000-220000000002-200000000
χ5822-2-222-222-22-2-22-222-2-222-22200000000000000-22-22-22-200-2200000-22-2200000000000000-22000000000-2200000000
χ5922-2-222-222-22-2-22-222-2-222-22200000000000000-22-2-22-22002-2000002-22-2000000000000002-2000000000-2200000000
χ6022-2-222-222-22-2-22-222-2-222-22200000000000000-22-2-22-2200-2200000-22-22000000000000002-20000000002-200000000
χ61444444-4-4-4-444440000-4-4-4-400000000000000000004-4-44000000000000000000000000000000000000000000000000
χ62444444-4-4-4-444440000-4-4-4-40000000000000000000-444-4000000000000000000000000000000000000000000000000
χ6344444-24444-2-2-2-2-4-4-4-4-2-2-2-222440000-2-2-2-2000022200000000-40000000000220000000000000000000000000000000
χ6444444-24444-2-2-2-2-4-4-4-4-2-2-2-222-4-40000222200002220000000040000000000-2-20000000000000000000000000000000
χ65444-4-444-44-444-4-4-44-44-4-4444400000000000000-4-440000000000000000000000000000000000000000000000000000
χ66444-4-44-44-4444-4-4000044-4-40000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ67444-4-44-44-4444-4-4000044-4-400000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ68444-4-4-24-44-4-2-222-44-4422-2-2-2-2000000−2i32i3−2i32i3000022-200000000000000000002i3−2i30000000000000000000000000000000
χ69444-4-4-24-44-4-2-222-44-4422-2-2-2-20000002i3−2i32i3−2i3000022-20000000000000000000−2i32i30000000000000000000000000000000
χ7044-44-4444-4-44-44-40000-44-44000000000000−2i22i22i2−2i20000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ7144-44-4444-4-44-44-40000-44-440000000000002i2−2i2−2i22i200000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ7244-44-44-4-4444-44-4-4-4444-44-4-4-400000000000000-4440000000000000000000000000000000000000000000000000000
χ7344-44-4-244-4-4-22-2200002-22-200000000−2i32i32i3−2i3−2i22i22i2−2i2000000000000000000000000−666−6i2−i2−i2i200000000000000000000000
χ7444-44-4-244-4-4-22-2200002-22-200000000−2i32i32i3−2i32i2−2i2−2i22i20000000000000000000000006−6−66−i2i2i2−i200000000000000000000000
χ7544-44-4-244-4-4-22-2200002-22-2000000002i3−2i3−2i32i3−2i22i22i2−2i20000000000000000000000006−6−66i2−i2−i2i200000000000000000000000
χ7644-44-4-244-4-4-22-2200002-22-2000000002i3−2i3−2i32i32i2−2i2−2i22i2000000000000000000000000−666−6−i2i2i2−i200000000000000000000000
χ7744-44-4-2-4-444-22-2244-4-4-22-22-2-2004i−4i4i−4i00000000-222000000000−2i2i−2i2i000000000000000000000000000000000000000
χ7844-44-4-2-4-444-22-2244-4-4-22-22-2-200−4i4i−4i4i00000000-2220000000002i−2i2i−2i000000000000000000000000000000000000000
χ7944-44-4-2-4-444-22-22-4-444-22-2222000000000000002-2-2000000000000023−23−232300000000000000000000000000000000000
χ8044-44-4-2-4-444-22-22-4-444-22-2222000000000000002-2-20000000000000−232323−2300000000000000000000000000000000000
χ8144-4-44-24-4-44-222-20000-222-2004-40000-2-22222−2222−220000000000000000000022−2200−22−22−22−2200000000000000000000000
χ8244-4-44-24-4-44-222-20000-222-2004-40000-2-222−2222−222200000000000000000000−2222002−22−22−22−200000000000000000000000
χ8344-4-44-24-4-44-222-20000-222-200-44000022-2-222−2222−2200000000000000000000−2222002−22−2−22−2200000000000000000000000
χ8444-4-44-24-4-44-222-20000-222-200-44000022-2-2−2222−22220000000000000000000022−2200−22−222−22−200000000000000000000000
χ8544-4-44-2-444-4-222-24-4-442-2-2222004-4-4400000000-22-2000000000-222-2000000000000000000000000000000000000000
χ8644-4-44-2-444-4-222-24-4-442-2-222200-444-400000000-22-20000000002-2-22000000000000000000000000000000000000000
χ8744-4-44-2-444-4-222-2-444-42-2-22-2-2000000000000002-220000004-400000-22-2200000000000000000000000000000000000
χ8844-4-44-2-444-4-222-2-444-42-2-22-2-2000000000000002-22000000-44000002-22-200000000000000000000000000000000000
χ8988888-4-8-8-8-8-4-4-4-40000444400000000000000000000000000000000000000000000000000000000000000000000000
χ90888-8-8-4-88-88-4-4440000-4-44400000000000000000000000000000000000000000000000000000000000000000000000
χ9116-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9216-16000-8000080000000000046−46000000000000000000000000000000000000000000000000000000000000000000000
χ9316-16000-80000800000000000−4646000000000000000000000000000000000000000000000000000000000000000000000

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