Finite Group Databasebeta

← Group #72270350

Character table — Group #72270350

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222222244444444444448888888888888888812121212161616161616161616161616161616161616161616161616162424242424242424323232323248484848484848484896
order122223444466668888121212122424244444661212161616162424242244448881212121212121212161624244848484848484848448816161616412122424224488816164
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1111-1-1-1-1111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ511111111111111111111111111-1-1-1-1111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ611111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ711111111111111111111111111-1-1-1-11111-1-1-1-11111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111-1-11
χ811111111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1
χ9111111111111111111111111-1-11111-1-1-1-111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-111-1-111-111-1-1-1
χ10111111111111111111111111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-11-1-1111
χ11111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111-1-1-1-111-1-1-1111
χ12111111111111111111111111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11111111-1-111-1-1111-1-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111111-1-111-1-1-1-1-1-1-11
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-11111111-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-11111-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-111-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1-111-1-1111-1-1-1-11
χ1722222222222222-2-2-2-22222-2-222000022220000-2-2-2222200-2000000000000-2-20000000022-2-20000000000000-200000
χ1822222222222222-2-2-2-22222-2-222000022220000-2-2-2-2-2-2-200-2000000000000-2-200000000-2-2220000000000000200000
χ1922222222222222-2-2-2-22222-2-2-2-20000-2-2-2-20000-2-2-222220020000000000002200000000-2-2-2-20000000000000200000
χ2022222222222222-2-2-2-22222-2-2-2-20000-2-2-2-20000-2-2-2-2-2-2-2002000000000000220000000022220000000000000-200000
χ2122222-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-12222-1-1-1000022222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-10000222-2-2-1-1-1-1-1-1-1-1-2-2-1-11111111100000000-211110000000000
χ2322222-12222-1-1-1-12222-1-1-1-1-1-122-2-2-2-2-1-1-1-12222-1-1-10000-2-22-2-21111111122-1-1-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222-12222-1-1-1-12222-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-1-1-10000-2-222211111111-2-2-1-111111111000000002-1-1-1-10000000000
χ2522222-12222-1-1-1-12222-1-1-1-1-1-1-2-2222211112222-1-1-10000-2-2-222-1-1-1-11111-2-2111111-1-1-1-100000000-211-1-10000000000
χ2622222-12222-1-1-1-12222-1-1-1-1-1-1-2-222221111-2-2-2-2-1-1-10000-2-2-2-2-2-1-1-1-111112211-1-1-1-11111000000002-1-1110000000000
χ2722222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-211112222-1-1-1000022-2-2-21111-1-1-1-1-2-2111111-1-1-1-1000000002-1-1110000000000
χ2822222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-21111-2-2-2-2-1-1-1000022-2221111-1-1-1-12211-1-1-1-1111100000000-211-1-10000000000
χ29222-2-222-22-22-22-2-2-2222-22-2-2-2002i2i−2i−2i000000002-220000000002i2i−2i−2i0000000000000000000022-2-200000000002i−2i000
χ30222-2-222-22-22-22-2-2-2222-22-2-2-2002i2i−2i−2i000000002-220000000002i2i−2i−2i00000000000000000000-2-2220000000000−2i2i000
χ31222-2-222-22-22-22-2-2-2222-22-2-2-200−2i−2i2i2i000000002-22000000000−2i−2i2i2i0000000000000000000022-2-20000000000−2i2i000
χ32222-2-222-22-22-22-2-2-2222-22-2-2-200−2i−2i2i2i000000002-22000000000−2i−2i2i2i00000000000000000000-2-22200000000002i−2i000
χ3322-22-22-222-222-2-2-22-22-222-222002i−2i2i−2i000022-2-2-2-2200000002i−2i2i−2i2i−2i00000000000022-2-2000000000002i−2i0000000000
χ3422-22-22-222-222-2-2-22-22-222-222002i−2i2i−2i0000-2-222-2-220000000−2i2i2i−2i2i−2i000000000000-2-22200000000000−2i2i0000000000
χ3522-22-22-222-222-2-2-22-22-222-22200−2i2i−2i2i000022-2-2-2-220000000−2i2i−2i2i−2i2i00000000000022-2-200000000000−2i2i0000000000
χ3622-22-22-222-222-2-2-22-22-222-22200−2i2i−2i2i0000-2-222-2-2200000002i−2i−2i2i−2i2i000000000000-2-222000000000002i−2i0000000000
χ3722-22-2-1-222-2-1-111-22-221-1-11-1-1002i−2i2i−2i−i3i3−i3i322-2-211-100000002i−2i−ii−ii33−3−300−i3i3−i3−i3i3i3-1-1110000000003−3−ii0000000000
χ3822-22-2-1-222-2-1-111-22-221-1-11-1-1002i−2i2i−2i−i3i3−i3i3-2-22211-10000000−2i2i−ii−ii33−3−300−i3i3i3i3−i3−i311-1-1000000000−33i−i0000000000
χ3922-22-2-1-222-2-1-111-22-221-1-11-1-1002i−2i2i−2ii3−i3i3−i322-2-211-100000002i−2i−ii−ii−3−33300i3−i3i3i3−i3−i3-1-111000000000−33−ii0000000000
χ4022-22-2-1-222-2-1-111-22-221-1-11-1-1002i−2i2i−2ii3−i3i3−i3-2-22211-10000000−2i2i−ii−ii−3−33300i3−i3−i3−i3i3i311-1-10000000003−3i−i0000000000
χ4122-22-2-1-222-2-1-111-22-221-1-11-1-100−2i2i−2i2i−i3i3−i3i322-2-211-10000000−2i2ii−ii−i−3−33300−i3i3−i3−i3i3i3-1-111000000000−33i−i0000000000
χ4222-22-2-1-222-2-1-111-22-221-1-11-1-100−2i2i−2i2i−i3i3−i3i3-2-22211-100000002i−2ii−ii−i−3−33300−i3i3i3i3−i3−i311-1-10000000003−3−ii0000000000
χ4322-22-2-1-222-2-1-111-22-221-1-11-1-100−2i2i−2i2ii3−i3i3−i322-2-211-10000000−2i2ii−ii−i33−3−300i3−i3i3i3−i3−i3-1-1110000000003−3i−i0000000000
χ4422-22-2-1-222-2-1-111-22-221-1-11-1-100−2i2i−2i2ii3−i3i3−i3-2-22211-100000002i−2ii−ii−i33−3−300i3−i3−i3−i3i3i311-1-1000000000−33−ii0000000000
χ4522-2-22222-2-22-2-22000022-2-2002-2000022-2-2−i2i2−i2i200022-2-20000000000000−i2i200−i2i2−i2i2−i2i2−i2i22-200−i2i2−i2i2000000000000−i2i20
χ4622-2-22222-2-22-2-22000022-2-2002-2000022-2-2−i2i2−i2i2000-2-2220000000000000−i2i200−i2i2−i2i2−i2i2−i2i2-2200i2−i2i2−i2000000000000i2−i20
χ4722-2-22222-2-22-2-22000022-2-2002-2000022-2-2i2−i2i2−i200022-2-20000000000000i2−i200i2−i2i2−i2i2−i2i2−i22-200i2−i2i2−i2000000000000i2−i20
χ4822-2-22222-2-22-2-22000022-2-2002-2000022-2-2i2−i2i2−i2000-2-2220000000000000i2−i200i2−i2i2−i2i2−i2i2−i2-2200−i2i2−i2i2000000000000−i2i20
χ4922-2-22222-2-22-2-22000022-2-200-220000-2-222−i2i2−i2i200022-2-20000000000000i2−i200i2−i2i2−i2−i2i2−i2i2-2200−i2i2−i2i2000000000000i2−i20
χ5022-2-22222-2-22-2-22000022-2-200-220000-2-222−i2i2−i2i2000-2-2220000000000000i2−i200i2−i2i2−i2−i2i2−i2i22-200i2−i2i2−i2000000000000−i2i20
χ5122-2-22222-2-22-2-22000022-2-200-220000-2-222i2−i2i2−i200022-2-20000000000000−i2i200−i2i2−i2i2i2−i2i2−i2-2200i2−i2i2−i2000000000000−i2i20
χ5222-2-22222-2-22-2-22000022-2-200-220000-2-222i2−i2i2−i2000-2-2220000000000000−i2i200−i2i2−i2i2i2−i2i2−i22-200−i2i2−i2i2000000000000i2−i20
χ5322-2-222-2-2222-2-222-2-22-2-222-2-2002-2-2200000000-2222-22-2000002-2-220000000000000000002-2000000000002-2000000
χ5422-2-222-2-2222-2-222-2-22-2-222-2-2002-2-2200000000-222-22-22000002-2-22000000000000000000-2200000000000-22000000
χ5522-2-222-2-2222-2-222-2-22-2-222-2-200-222-200000000-2222-22-200000-222-20000000000000000002-200000000000-22000000
χ5622-2-222-2-2222-2-222-2-22-2-222-2-200-222-200000000-222-22-2200000-222-2000000000000000000-22000000000002-2000000
χ5722-2-222-2-2222-2-22-222-2-2-22222000000000000002-2-22-22-22-200000002-22-200000000000000-220000000002-200000000
χ5822-2-222-2-2222-2-22-222-2-2-22222000000000000002-2-22-22-2-220000000-22-2200000000000000-22000000000-2200000000
χ5922-2-222-2-2222-2-22-222-2-2-22222000000000000002-2-2-22-222-200000002-22-2000000000000002-2000000000-2200000000
χ6022-2-222-2-2222-2-22-222-2-2-22222000000000000002-2-2-22-22-220000000-22-22000000000000002-20000000002-200000000
χ61444444-4-4-4-444440000-4-4-4-400000000000000000004-4-44000000000000000000000000000000000000000000000000
χ62444444-4-4-4-444440000-4-4-4-40000000000000000000-444-4000000000000000000000000000000000000000000000000
χ6344444-24444-2-2-2-2-4-4-4-4-2-2-2-222440000-2-2-2-20000222000000-4000000000000220000000000000000000000000000000
χ6444444-24444-2-2-2-2-4-4-4-4-2-2-2-222-4-40000222200002220000004000000000000-2-20000000000000000000000000000000
χ65444-4-444-44-44-44-444-4-44-44-44400000000000000-44-40000000000000000000000000000000000000000000000000000
χ66444-4-44-44-444-44-40000-44-44000000000000−2i22i22i2−2i20000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ67444-4-44-44-444-44-40000-44-440000000000002i2−2i2−2i22i200000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ68444-4-4-24-44-4-22-2244-4-4-22-22-2-2000000000000002-22000000000000023−23−232300000000000000000000000000000000000
χ69444-4-4-24-44-4-22-2244-4-4-22-22-2-2000000000000002-220000000000000−232323−2300000000000000000000000000000000000
χ70444-4-4-24-44-4-22-22-4-444-22-2222004i4i−4i−4i00000000-22-2000000000−2i−2i2i2i000000000000000000000000000000000000000
χ71444-4-4-24-44-4-22-22-4-444-22-222200−4i−4i4i4i00000000-22-20000000002i2i−2i−2i000000000000000000000000000000000000000
χ72444-4-4-2-44-44-22-2200002-22-200000000−2i32i32i3−2i3−2i22i22i2−2i2000000000000000000000000−666−6i2−i2−i2i200000000000000000000000
χ73444-4-4-2-44-44-22-2200002-22-200000000−2i32i32i3−2i32i2−2i2−2i22i20000000000000000000000006−6−66−i2i2i2−i200000000000000000000000
χ74444-4-4-2-44-44-22-2200002-22-2000000002i3−2i3−2i32i3−2i22i22i2−2i20000000000000000000000006−6−66i2−i2−i2i200000000000000000000000
χ75444-4-4-2-44-44-22-2200002-22-2000000002i3−2i3−2i32i32i2−2i2−2i22i2000000000000000000000000−666−6−i2i2i2−i200000000000000000000000
χ7644-44-444-4-4444-4-400004-4-440000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ7744-44-444-4-4444-4-400004-4-4400000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ7844-44-44-444-444-4-44-44-4-444-4-4-40000000000000044-40000000000000000000000000000000000000000000000000000
χ7944-44-4-2-444-4-2-2224-44-42-2-2222000000−2i32i3−2i32i30000-2-2200000000000000000002i3−2i30000000000000000000000000000000
χ8044-44-4-2-444-4-2-2224-44-42-2-22220000002i3−2i32i3−2i30000-2-220000000000000000000−2i32i30000000000000000000000000000000
χ8144-4-44-244-4-4-222-20000-2-222004-40000-2-222−2i22i2−2i22i200000000000000000000−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000
χ8244-4-44-244-4-4-222-20000-2-222004-40000-2-2222i2−2i22i2−2i2000000000000000000002i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000
χ8344-4-44-244-4-4-222-20000-2-22200-44000022-2-2−2i22i2−2i22i2000000000000000000002i2−2i200−i2i2−i2i2i2−i2i2−i200000000000000000000000
χ8444-4-44-244-4-4-222-20000-2-22200-44000022-2-22i2−2i22i2−2i200000000000000000000−2i22i200i2−i2i2−i2−i2i2−i2i200000000000000000000000
χ8544-4-44-2-4-444-222-24-4-4422-2-222004-4-44000000002-2-2000000000-222-2000000000000000000000000000000000000000
χ8644-4-44-2-4-444-222-24-4-4422-2-22200-444-4000000002-2-20000000002-2-22000000000000000000000000000000000000000
χ8744-4-44-2-4-444-222-2-444-422-2-2-2-200000000000000-22200004-40000000-22-2200000000000000000000000000000000000
χ8844-4-44-2-4-444-222-2-444-422-2-2-2-200000000000000-2220000-4400000002-22-200000000000000000000000000000000000
χ8988888-4-8-8-8-8-4-4-4-40000444400000000000000000000000000000000000000000000000000000000000000000000000
χ9088-88-8-48-8-88-4-4440000-444-400000000000000000000000000000000000000000000000000000000000000000000000
χ9116-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9216-16000-8000080000000000046−46000000000000000000000000000000000000000000000000000000000000000000000
χ9316-16000-80000800000000000−4646000000000000000000000000000000000000000000000000000000000000000000000

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