Finite Group Databasebeta

← Group #72267872

Character table — Group #72267872

Order 10240.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1111555555555555404040404040404040404040808080808080160160160160160160160160160160160160160160160160160160160160160160160160320320320320512512512512512512512512
order1222222222222222444444444444444444888888888888888888888888444455101010101010
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
χ544-4-444444-4-44-4-4-4-400000000000000000000000000000000002222-2-2-2-20000-1-111-111-1
χ644-4-444444-4-44-4-4-4-40000000000000000000000000000000000-2-2-2-222220000-1-111-111-1
χ74-44-4444-4-444-44-4-4-4000000000000000000000000002222-2-2-2-2000000000000-1-11-111-11
χ84-44-4444-4-444-44-4-4-400000000000000000000000000-2-2-2-22222000000000000-1-11-111-11
χ94-4-44444-4-4-4-4-4-44440000000000000000002i2i2i2i−2i−2i−2i−2i00000000000000000000-1-1-111-111
χ104-4-44444-4-4-4-4-4-4444000000000000000000−2i−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
χ1788-8-888888-8-88-8-8-8-800000000000000000000000000000000000000000000001−521+52−1+52−1+521−52−1−52−1−521+52
χ1888-8-888888-8-88-8-8-8-800000000000000000000000000000000000000000000001+521−52−1−52−1−521+52−1+52−1+521−52
χ198-88-8888-8-888-88-8-8-800000000000000000000000000000000000000000000001−521+52−1+521−52−1+52−1−521+52−1−52
χ208-88-8888-8-888-88-8-8-800000000000000000000000000000000000000000000001+521−52−1−521+52−1−52−1+521−52−1+52
χ218-8-88888-8-8-8-8-8-888800000000000000000000000000000000000000000000001−521+521−52−1+52−1+521+52−1−52−1−52
χ228-8-88888-8-8-8-8-8-888800000000000000000000000000000000000000000000001+521−521+52−1−52−1−521−52−1+52−1+52
χ231010101022-62-62-62222-62222-2-22222-2-2-2-2-2-222000000000000000022-2-222-2-2000000000000
χ241010101022-62-62-62222-62222-2-22222-2-2-2-2-2-2220000000000000000-2-222-2-222000000000000
χ251010101022-62-62-62222-622-2-22222-2-222-2-222-2-20000000022-2-222-2-200000000000000000000
χ261010101022-62-62-62222-622-2-22222-2-222-2-222-2-200000000-2-222-2-22200000000000000000000
χ271010101022-62-62-62222-6-2-22222-2-2222222-2-2-2-20000000000000000000000002-2-2200000000
χ281010101022-62-62-62222-6-2-22222-2-2222222-2-2-2-2000000000000000000000000-222-200000000
χ291010101022-62-62-62222-6-2-2-2-2-2-2-2-2-2-2-2-22222222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ301010101022-62-62-62222-6-2-2-2-2-2-2-2-2-2-2-2-2222222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ311010-10-102-62226-2-6-26-2-200224-400-2-24-4002-2002−22−22−22−22−22−22−22−200000000000000000000
χ321010-10-102-62226-2-6-26-2-200224-400-2-24-4002-200−22−22−22−22−22−22−22−2200000000000000000000
χ331010-10-102-62226-2-6-26-2-20022-4400-2-2-44002-2002−22−22−22−2−22−22−22−2200000000000000000000
χ341010-10-102-62226-2-6-26-2-20022-4400-2-2-44002-200−22−22−22−222−22−22−22−200000000000000000000
χ351010-10-10-622-62-2-226-26-24i−4i-2-2004i−4i2200002-200i2−i2−i2i2i2−i2−i2i22−2−222−2−2200000000000000000000
χ361010-10-10-622-62-2-226-26-24i−4i-2-2004i−4i2200002-200−i2i2i2−i2−i2i2i2−i2−222−2−222−200000000000000000000
χ371010-10-10-622-62-2-226-26-2−4i4i-2-200−4i4i2200002-200i2−i2−i2i2i2−i2−i2i2−222−2−222−200000000000000000000
χ381010-10-10-622-62-2-226-26-2−4i4i-2-200−4i4i2200002-200−i2i2i2−i2−i2i2i2−i22−2−222−2−2200000000000000000000
χ3910-1010-102-62-2-2-62626-2-24i−4i00-2-2−4i4i002200002-2i2−i2i2−i2−i2i2−i2i2000000002−22−22−22−2000000000000
χ4010-1010-102-62-2-2-62626-2-24i−4i00-2-2−4i4i002200002-2−i2i2−i2i2i2−i2i2−i200000000−22−22−22−22000000000000
χ4110-1010-102-62-2-2-62626-2-2−4i4i00-2-24i−4i002200002-2i2−i2i2−i2−i2i2−i2i200000000−22−22−22−22000000000000
χ4210-1010-102-62-2-2-62626-2-2−4i4i00-2-24i−4i002200002-2−i2i2−i2i2i2−i2i2−i2000000002−22−22−22−2000000000000
χ4310-1010-10-6226-222-2-6-26-2004-422004-4-2-200002-22−2−22−222−2000000002−2−222−2−22000000000000
χ4410-1010-10-6226-222-2-6-26-2004-422004-4-2-200002-2−222−22−2−2200000000−222−2−222−2000000000000
χ4510-1010-10-6226-222-2-6-26-200-442200-44-2-200002-22−2−22−222−200000000−222−2−222−2000000000000
χ4610-1010-10-6226-222-2-6-26-200-442200-44-2-200002-2−222−22−2−22000000002−2−222−2−22000000000000
χ4710-10-10102-62-2-26-26-2-622-2-24-40022-44002-20000000000002−22−2−22−222−22−2−22−22000000000000
χ4810-10-10102-62-2-26-26-2-622-2-24-40022-44002-2000000000000−22−222−22−2−22−222−22−2000000000000
χ4910-10-10102-62-2-26-26-2-622-2-2-4400224-4002-20000000000002−22−2−22−22−22−222−22−2000000000000
χ5010-10-10102-62-2-26-26-2-622-2-2-4400224-4002-2000000000000−22−222−22−22−22−2−22−22000000000000
χ5110-10-1010-6226-2-2-2-262-62-2-2004-42200-44-220000000000002−2−22−222−2−222−22−2−22000000000000
χ5210-10-1010-6226-2-2-2-262-62-2-2004-42200-44-22000000000000−222−22−2−222−2−22−222−2000000000000
χ5310-10-1010-6226-2-2-2-262-62-2-200-4422004-4-220000000000002−2−22−222−22−2−22−222−2000000000000
χ5410-10-1010-6226-2-2-2-262-62-2-200-4422004-4-22000000000000−222−22−2−22−222−22−2−22000000000000
χ55202020204-12444-124-124-124400000000000000000000000000000000000000000022-2-200000000
χ56202020204-12444-124-124-1244000000000000000000000000000000000000000000-2-22200000000
χ5720202020-1244-124444-124-1240000000000000000000000000000000000000000002-22-200000000
χ5820202020-1244-124444-124-124000000000000000000000000000000000000000000-22-2200000000
χ592020-20-2044-124-12-4124-4-4-412000000000000000000000000000000000022-2-2-2-222000000000000
χ602020-20-2044-124-12-4124-4-4-4120000000000000000000000000000000000-2-22222-2-2000000000000
χ612020-20-204-1244412-4-12-412-4-400-4-40000440000-4400000000000000000000000000000000000000
χ622020-20-20-1244-124-4-4412-412-400440000-4-40000-4400000000000000000000000000000000000000
χ6320-2020-2044-12-4124-12-44-4-4120000000000000000000000000022-2-2-2-22200000000000000000000
χ6420-2020-2044-12-4124-12-44-4-41200000000000000000000000000-2-22222-2-200000000000000000000
χ6520-2020-204-124-4-4-12412412-4-40000440000-4-40000-44000000000000000000000000000000000000
χ6620-2020-20-124412-444-4-12-412-40000-4-40000440000-44000000000000000000000000000000000000
χ6720-20-202044-12-412-412-4-444-1200000000000000000022-2-2-2-2220000000000000000000000000000
χ6820-20-202044-12-412-412-4-444-12000000000000000000-2-22222-2-20000000000000000000000000000
χ6920-20-20204-124-4-412-412-4-1244440000-4-40000-440000000000000000000000000000000000000000
χ7020-20-2020-124412-4-4-4-4124-124440000-4-400004-40000000000000000000000000000000000000000

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