Finite Group Databasebeta

← Group #72267842

Character table — Group #72267842

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11113333333333336666881616242424242424242424244848484848484848484848484848969696969696969696969696969696969696969696969696128128128128192192192192256256256256256256
order12222222222222222222444444444444444444444444444488888888888888888888888836662444121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ31111111111111111111111-1-1111111111111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ41111111111111111111111-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ5222222222222222222222222222222222222222222222222000000000000000000000000-1-1-1-10000-1-1-1-1-1-1
χ62222222222222222222222-2-2222222222222-2-222-2-2-2-2-2-2-2-2000000000000000000000000-1-1-1-10000-1-11111
χ722222222222222222222-2-200-2-2-222-2-2-222-2-200220000000000000000000000000000000022220000-2-20000
χ822222222222222222222-2-200-2-2-222-2-2-222-2-2002200000000000000000000000000000000-1-1-1-1000011−i3−i3i3i3
χ922222222222222222222-2-200-2-2-222-2-2-222-2-2002200000000000000000000000000000000-1-1-1-1000011i3i3−i3−i3
χ1022-2-222-2-2-2-2-2-2222222-2-20000000-2-20002200002-200000000−i2−i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i20000000022-2-20000000000
χ1122-2-222-2-2-2-2-2-2222222-2-20000000-2-20002200002-200000000i2i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i20000000022-2-20000000000
χ122-22-2-2-2222-2-2-2222-22-2-222-22i−2i20000-20000002i−2i000000000000000022−2−20022−2−2−i2−i2−i2−i2i2i2i2i2-11-1100001-1i−ii−i
χ132-22-2-2-2222-2-2-2222-22-2-222-22i−2i20000-20000002i−2i0000000000000000−2−22200−2−222i2i2i2i2−i2−i2−i2−i2-11-1100001-1i−ii−i
χ142-22-2-2-2222-2-2-2222-22-2-222-2−2i2i20000-2000000−2i2i000000000000000022−2−20022−2−2i2i2i2i2−i2−i2−i2−i2-11-1100001-1−ii−ii
χ152-22-2-2-2222-2-2-2222-22-2-222-2−2i2i20000-2000000−2i2i0000000000000000−2−22200−2−222−i2−i2−i2−i2i2i2i2i2-11-1100001-1−ii−ii
χ163333333333333333333333333-1-1-1-13-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-100001111000000
χ173333333333333333333333333-1-1-1-13-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111110000-1-1-1-1000000
χ183333333333333333333333-3-33-1-1-1-13-1-1-1-1-1-1-3-3-1-111111111111111-1-1-1-111-1-1-1-1111111110000-1-1-1-1000000
χ193333333333333333333333-3-33-1-1-1-13-1-1-1-1-1-1-3-3-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-100001111000000
χ2044-4-444-4-4-4-4-4-4444444-4-40000000-4-40004400004-400000000000000000000000000000000-2-2220000000000
χ214-44-4-4-4444-4-4-4444-44-4-444-44i−4i40000-40000004i−4i00000000000000000000000000000000001-11-10000-11−ii−ii
χ224-44-4-4-4444-4-4-4444-44-4-444-4−4i4i40000-4000000−4i4i00000000000000000000000000000000001-11-10000-11i−ii−i
χ234-44-4-4-4444-4-4-4444-44-4-44-4400-4000040000000000000000000000000000000000000000001-11-100001-13−3−33
χ244-44-4-4-4444-4-4-4444-44-4-44-4400-4000040000000000000000000000000000000000000000001-11-100001-1−333−3
χ254-44-4-4-4444-4-4-4444-44-4-44-4400-400004000000000000000000000000000000000000000000-22-220000-220000
χ264-4-44-4-4-4-4-4444444-44-44-400000000000000000000000000000000002i2i−2i−2i00−2i−2i2i2i00000000-222-20000000000
χ274-4-44-4-4-4-4-4444444-44-44-40000000000000000000000000000000000−2i−2i2i2i002i2i−2i−2i00000000-222-20000000000
χ2866666666666666666666-6-600-622-2-2-622-2-22200-2-20000000000000000000000000000000000000000000000
χ296666-2-26-2-26-2-26-2-26-2-2-2-26600-222-2-2-222-2-2-2-20022000000002222-2-20000-2-200000000000000000000000000
χ306666-2-26-2-26-2-26-2-26-2-2-2-26600-222-2-2-222-2-2-2-2002200000000-2-2-2-22200002200000000000000000000000000
χ316666-2-26-2-26-2-26-2-26-2-2-2-26600-2-2-222-2-2-2222200-2-200000000000000000000000000000000000022-2-2000000
χ326666-2-26-2-26-2-26-2-26-2-2-2-26600-2-2-222-2-2-2222200-2-2000000000000000000000000000000000000-2-222000000
χ336666-2-26-2-26-2-26-2-26-2-2-2-2-6-6002222222222-2-200-2-200000000000000000000000022-2-222-2-200000000000000
χ346666-2-26-2-26-2-26-2-26-2-2-2-2-6-6002222222222-2-200-2-2000000000000000000000000-2-222-2-22200000000000000
χ356666-2-26-2-26-2-26-2-26-2-2-2-2-6-6002-2-2-2-22-2-2-2-2220022000000000000002i−2i2i−2i002i−2i2i−2i0000000000000000000000
χ366666-2-26-2-26-2-26-2-26-2-2-2-2-6-6002-2-2-2-22-2-2-2-222002200000000000000−2i2i−2i2i00−2i2i−2i2i0000000000000000000000
χ3766-6-666-6-6-6-6-6-6666666-6-6000000022000-2-20000-2200000000−i2−i2i2i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i20000000000000000000000
χ3866-6-666-6-6-6-6-6-6666666-6-6000000022000-2-20000-2200000000i2i2−i2−i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i20000000000000000000000
χ3966-6-6-2-2-622-6226-2-26-2-222000004i−4i2204i−4i-2-200002-200000000−i2−i2i2i2i2i22−22−2−i2−i2−22−220000000000000000000000
χ4066-6-6-2-2-622-6226-2-26-2-222000004i−4i2204i−4i-2-200002-200000000i2i2−i2−i2−i2−i2−22−22i2i22−22−20000000000000000000000
χ4166-6-6-2-2-622-6226-2-26-2-22200000−4i4i220−4i4i-2-200002-200000000−i2−i2i2i2i2i2−22−22−i2−i22−22−20000000000000000000000
χ4266-6-6-2-2-622-6226-2-26-2-22200000−4i4i220−4i4i-2-200002-200000000i2i2−i2−i2−i2−i22−22−2i2i2−22−220000000000000000000000
χ436-66-6226-2-2-6226-2-2-6-222-2-660020000-200000000002222-2-2-2-2000000−i2i2i2−i200−i2i2i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ446-66-6226-2-2-6226-2-2-6-222-2-660020000-200000000002222-2-2-2-2000000i2−i2−i2i200i2−i2−i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ456-66-6226-2-2-6226-2-2-6-222-2-660020000-20000000000-2-2-2-22222000000−i2i2i2−i200−i2i2i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ466-66-6226-2-2-6226-2-2-6-222-2-660020000-20000000000-2-2-2-22222000000i2−i2−i2i200i2−i2−i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ476-6-662-622-6-26-2-26-22-22-2200000-2-200022002-2000022-2-222-2-22−22−22−200002−200002−22−22−22−200000000000000
χ486-6-662-622-6-26-2-26-22-22-2200000-2-200022002-2000022-2-222-2-2−22−22−220000−220000−22−22−22−2200000000000000
χ496-6-662-622-6-26-2-26-22-22-2200000-2-200022002-20000-2-222-2-2222−22−22−200002−20000−22−22−22−2200000000000000
χ506-6-662-622-6-26-2-26-22-22-2200000-2-200022002-20000-2-222-2-222−22−22−220000−2200002−22−22−22−200000000000000
χ516-6-66-622-62-2-26-2-262-22-2200000-2-20002200-2200002-22-22-22-22−22−2−220000−2200002−2−222−2−2200000000000000
χ526-6-66-622-62-2-26-2-262-22-2200000-2-20002200-2200002-22-22-22-2−22−222−200002−20000−222−2−222−200000000000000
χ536-6-66-622-62-2-26-2-262-22-2200000-2-20002200-220000-22-22-22-222−22−2−220000−220000−222−2−222−200000000000000
χ546-6-66-622-62-2-26-2-262-22-2200000-2-20002200-220000-22-22-22-22−22−222−200002−200002−2−222−2−2200000000000000
χ558-8-88-8-8-8-8-8888888-88-88-800000000000000000000000000000000000000000000000000002-2-220000000000
χ561212121212-4-412-4-4-412-4-412-4-4-4-4-4000000000000000000000000000000000000000000000000000000002-2-22000000
χ571212121212-4-412-4-4-412-4-412-4-4-4-4-400000000000000000000000000000000000000000000000000000000-222-2000000
χ5812121212-412-4-412-412-4-412-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000002-22-2000000
χ5912121212-412-4-412-412-4-412-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000-22-22000000
χ6012121212-4-4-4-4-4-4-4-4-4-4-4-4444400660004-40004-400-2-2002-2-222-2-2200000000000000000000000000000000000000
χ6112121212-4-4-4-4-4-4-4-4-4-4-4-444440066000-44000-4400-2-200-222-2-222-200000000000000000000000000000000000000
χ6212121212-4-4-4-4-4-4-4-4-4-4-4-4444400-6-60004-40004-4002200-222-2-222-200000000000000000000000000000000000000
χ6312121212-4-4-4-4-4-4-4-4-4-4-4-4444400-6-6000-44000-440022002-2-222-2-2200000000000000000000000000000000000000
χ641212-12-1212-44-12444-12-4-412-4-4-444000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ651212-12-1212-44-12444-12-4-412-4-4-44400000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ661212-12-12-41244-124-124-412-4-4-4-444000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000
χ671212-12-12-41244-124-124-412-4-4-4-44400000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000
χ681212-12-12-4-4444444-4-4-4-444-4-400000004-4000-44000000400-4-400400000000000000000000000000000000000000
χ691212-12-12-4-4444444-4-4-4-444-4-400000004-4000-44000000-4004400-400000000000000000000000000000000000000
χ701212-12-12-4-4444444-4-4-4-444-4-40000000-440004-400000004-400-44000000000000000000000000000000000000000
χ711212-12-12-4-4444444-4-4-4-444-4-40000000-440004-40000000-44004-4000000000000000000000000000000000000000
χ721212-12-12-4-4-1244-124412-4-412-4-4440000000-4-4000440000-440000000000000000000000000000000000000000000000
χ7312-1212-124412-4-4-124412-4-4-12-444-412-1200-40000400000000000000000000000000000000000000000000000000000000
χ7412-1212-1244-4-4-4444-4-4-444-4-44006i−6i04i−4i000−4i4i0000−2i2i002-2-22-222-200000000000000000000000000000000000000
χ7512-1212-1244-4-4-4444-4-4-444-4-44006i−6i0−4i4i0004i−4i0000−2i2i00-222-22-2-2200000000000000000000000000000000000000
χ7612-1212-1244-4-4-4444-4-4-444-4-4400−6i6i04i−4i000−4i4i00002i−2i00-222-22-2-2200000000000000000000000000000000000000
χ7712-1212-1244-4-4-4444-4-4-444-4-4400−6i6i0−4i4i0004i−4i00002i−2i002-2-22-222-200000000000000000000000000000000000000
χ7812-1212-124-12-4-4124-124-412-44-444-400000000000000000000000000002i−2i−2i2i2i−2i0000−2i2i00000000000000000000000000
χ7912-1212-124-12-4-4124-124-412-44-444-40000000000000000000000000000−2i2i2i−2i−2i2i00002i−2i00000000000000000000000000
χ8012-1212-12-124-412-444-12-4-4124-444-400000000000000000000000000002i−2i−2i2i−2i2i00002i−2i00000000000000000000000000
χ8112-1212-12-124-412-444-12-4-4124-444-40000000000000000000000000000−2i2i2i−2i2i−2i0000−2i2i00000000000000000000000000
χ8212-12-121244-124412-4-412-4-4-12-44-4400000000000000000000000000000000002-2-2200-222-20000000000000000000000
χ8312-12-121244-124412-4-412-4-4-12-44-440000000000000000000000000000000000-222-2002-2-220000000000000000000000
χ8412-12-12124-1244-12-412-4-412-44-44-440000044000-4-400-4400000000000000000000000000000000000000000000000000
χ8512-12-1212-1244-124-4-412-4-4124-44-440000044000-4-4004-400000000000000000000000000000000000000000000000000
χ8624-24-242488888-8-8-8-8-8-888-88-8000000000000000000000000000000000000000000000000000000000000000000

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