Finite Group Databasebeta

← Group #72267833

Character table — Group #72267833

Order 10240.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1111555555555555404040404040404040404040808080808080160160160160160160160160160160160160160160160160160160160160160160160160320320320320512512512512512512512512
order1222222222222222444444444444444444888888888888888888888888244455101010101010
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ322222222222222222222222222222222220000000000000000000000000000−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52
χ422222222222222222222222222222222220000000000000000000000000000−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52
χ544-4-444-4-4-4-4-44444-400000000000000000000000000000000002i2i2i2i−2i−2i−2i−2i0000-1-111-111-1
χ644-4-444-4-4-4-4-44444-40000000000000000000000000000000000−2i−2i−2i−2i2i2i2i2i0000-1-111-111-1
χ74-44-4-4-444-4-4-4444-44000000000000000000000000002i2i2i2i−2i−2i−2i−2i000000000000-1-11-111-11
χ84-44-4-4-444-4-4-4444-4400000000000000000000000000−2i−2i−2i−2i2i2i2i2i000000000000-1-11-111-11
χ94-4-44-4-4-4-4444444-4-40000000000000000002i2i2i2i−2i−2i−2i−2i00000000000000000000-1-1-111-111
χ104-4-44-4-4-4-4444444-4-4000000000000000000−2i−2i−2i−2i2i2i2i2i00000000000000000000-1-1-111-111
χ1155555555555555551111-3-31111-3-31111-3-311111111-1-1-1-1-1-1-1-111111111-1-1-1-100000000
χ1255555555555555551111-3-31111-3-31111-3-3-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111100000000
χ13555555555555555511-3-31111-3-31111-3-3111111111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000
χ14555555555555555511-3-31111-3-31111-3-311-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000
χ155555555555555555-3-31111-3-31111-3-3111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111100000000
χ165555555555555555-3-31111-3-31111-3-31111-1-1-1-1-1-1-1-11111111111111111-1-1-1-100000000
χ1788-8-888-8-8-8-8-88888-800000000000000000000000000000000000000000000001−521+52−1+52−1+521−52−1−52−1−521+52
χ1888-8-888-8-8-8-8-88888-800000000000000000000000000000000000000000000001+521−52−1−52−1−521+52−1+52−1+521−52
χ198-88-8-8-888-8-8-8888-8800000000000000000000000000000000000000000000001−521+52−1+521−52−1+52−1−521+52−1−52
χ208-88-8-8-888-8-8-8888-8800000000000000000000000000000000000000000000001+521−52−1−521+52−1−52−1+521−52−1+52
χ218-8-88-8-8-8-8888888-8-800000000000000000000000000000000000000000000001−521+521−52−1+52−1+521+52−1−52−1−52
χ228-8-88-8-8-8-8888888-8-800000000000000000000000000000000000000000000001+521−521+52−1−52−1−521−52−1+52−1+52
χ23101010102-62-622-622-6222222-2-22222-2-2-2-2-2-222000000000000000022-2-222-2-2000000000000
χ24101010102-62-622-622-6222222-2-22222-2-2-2-2-2-2220000000000000000-2-222-2-222000000000000
χ25101010102-62-622-622-62222-2-22222-2-222-2-222-2-20000000022-2-222-2-200000000000000000000
χ26101010102-62-622-622-62222-2-22222-2-222-2-222-2-200000000-2-222-2-22200000000000000000000
χ27101010102-62-622-622-622-2-22222-2-2222222-2-2-2-20000000000000000000000002-2-2200000000
χ28101010102-62-622-622-622-2-22222-2-2222222-2-2-2-2000000000000000000000000-222-200000000
χ29101010102-62-622-622-622-2-2-2-2-2-2-2-2-2-2-2-22222222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ30101010102-62-622-622-622-2-2-2-2-2-2-2-2-2-2-2-2222222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ311010-10-10226-26-2-22-62-6-200-2-24-400224-4002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000000000
χ321010-10-10226-26-2-22-62-6-200-2-24-400224-4002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000000000
χ331010-10-10226-26-2-22-62-6-200-2-2-440022-44002-200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000000000
χ341010-10-10226-26-2-22-62-6-200-2-2-440022-44002-200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000000000
χ351010-10-10-62-2-2-26-2-622264i−4i22004i−4i-2-200002-2002−2−222−2−22−i2i2i2−i2−i2i2i2−i200000000000000000000
χ361010-10-10-62-2-2-26-2-622264i−4i22004i−4i-2-200002-200−222−2−222−2i2−i2−i2i2i2−i2−i2i200000000000000000000
χ371010-10-10-62-2-2-26-2-62226−4i4i2200−4i4i-2-200002-2002−2−222−2−22i2−i2−i2i2i2−i2−i2i200000000000000000000
χ381010-10-10-62-2-2-26-2-62226−4i4i2200−4i4i-2-200002-200−222−2−222−2−i2i2i2−i2−i2i2i2−i200000000000000000000
χ3910-1010-106-222-26-2-622-2-6004-4-2-2004-42200002-2i2−i2−i2i2−i2i2i2−i200000000i2−i2i2−i2i2−i2i2−i2000000000000
χ4010-1010-106-222-26-2-622-2-6004-4-2-2004-42200002-2−i2i2i2−i2i2−i2−i2i200000000−i2i2−i2i2−i2i2−i2i2000000000000
χ4110-1010-106-222-26-2-622-2-600-44-2-200-442200002-2i2−i2−i2i2−i2i2i2−i200000000−i2i2−i2i2−i2i2−i2i2000000000000
χ4210-1010-106-222-26-2-622-2-600-44-2-200-442200002-2−i2i2i2−i2i2−i2−i2i200000000i2−i2i2−i2i2−i2i2−i2000000000000
χ4310-1010-10-2-2-626-2-22-62624i−4i0022−4i4i00-2-200002-22−22−2−22−2200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ4410-1010-10-2-2-626-2-22-62624i−4i0022−4i4i00-2-200002-2−22−222−22−200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ4510-1010-10-2-2-626-2-22-6262−4i4i00224i−4i00-2-200002-22−22−2−22−2200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ4610-1010-10-2-2-626-2-22-6262−4i4i00224i−4i00-2-200002-2−22−222−22−200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ4710-10-10106-2-2-22-62-622-26-2-2004-42200-442-20000000000002−2−22−222−22−22−2−22−22000000000000
χ4810-10-10106-2-2-22-62-622-26-2-2004-42200-442-2000000000000−222−22−2−22−22−222−22−2000000000000
χ4910-10-10106-2-2-22-62-622-26-2-200-4422004-42-20000000000002−2−22−222−2−22−222−22−2000000000000
χ5010-10-10106-2-2-22-62-622-26-2-200-4422004-42-2000000000000−222−22−2−222−22−2−22−22000000000000
χ5110-10-1010-2-26-2-6222-626-2-2-24-40022-4400-220000000000002−22−2−22−222−2−22−222−2000000000000
χ5210-10-1010-2-26-2-6222-626-2-2-24-40022-4400-22000000000000−22−222−22−2−222−22−2−22000000000000
χ5310-10-1010-2-26-2-6222-626-2-2-2-4400224-400-220000000000002−22−2−22−22−222−22−2−22000000000000
χ5410-10-1010-2-26-2-6222-626-2-2-2-4400224-400-22000000000000−22−222−22−22−2−22−222−2000000000000
χ552020202044-124-12444-124-1240000000000000000000000000000000000000000002-22-200000000
χ562020202044-124-12444-124-124000000000000000000000000000000000000000000-22-2200000000
χ5720202020-124444-124-12444-1200000000000000000000000000000000000000000022-2-200000000
χ5820202020-124444-124-12444-12000000000000000000000000000000000000000000-2-22200000000
χ592020-20-204412-412-4-44-124-12-400440000-4-40000-4400000000000000000000000000000000000000
χ602020-20-204-12-412-4-41244-124-400000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ612020-20-204-12-412-4-41244-124-40000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ622020-20-20-124-4-4-412-4-124441200-4-40000440000-4400000000000000000000000000000000000000
χ6320-2020-2012-444-412-4-1244-4-120000440000-4-40000-44000000000000000000000000000000000000
χ6420-2020-20-4124-12-4-41244-12-44000000000000000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ6520-2020-20-4124-12-4-41244-12-4400000000000000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ6620-2020-20-4-4-12412-4-44-1241240000-4-40000440000-44000000000000000000000000000000000000
χ6720-20-202012-4-4-44-124-1244-412440000-4-40000-440000000000000000000000000000000000000000
χ6820-20-2020-412-41244-1244-12-4-400000000000000000022-2-2-2-2220000000000000000000000000000
χ6920-20-2020-412-41244-1244-12-4-4000000000000000000-2-22222-2-20000000000000000000000000000
χ7020-20-2020-4-412-4-12444-12412-4440000-4-400004-40000000000000000000000000000000000000000

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