Finite Group Databasebeta

← Group #12019916

Character table — Group #12019916

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1122222222222224444444444444444444444444444488888888888888888888881616161616161616161616161616161616161616404040404040404080808080
order122445588101010101010448881616161620202020202020202020202040404040404040401616404040408080808080808080808080808080808044442020202020202020202020202020202032323232323232322488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ6111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ7111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ911-11-11111-1-1-1-111i−ii−i-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i1-1i−i
χ1011-11-11111-1-1-1-111i−ii−i-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−iiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii-11−ii
χ1111-11-11111-1-1-1-111i−ii−i-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i-11−ii
χ1211-11-11111-1-1-1-111i−ii−i-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii−i−i−i−iiiii-1-1-1-11111-1-111−i−iii1-1i−i
χ1311-11-11111-1-1-1-111−ii−ii-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1-1−ii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii1-1−ii
χ1411-11-11111-1-1-1-111−ii−ii-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1-1−ii−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i-11i−i
χ1511-11-11111-1-1-1-111−ii−ii-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii-11i−iiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii-11i−i
χ1611-11-11111-1-1-1-111−ii−ii-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii-11i−iiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i1-1−ii
χ1722222222222222222222-2-2-2-222222222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ192222222-2-222222222-2-2-20000222222222222-2-2-2-2-2-2-2-200-2-2-2-20000000000000000000000000000000000002−22−22−22−20000
χ202222222-2-222222222-2-2-20000222222222222-2-2-2-2-2-2-2-200-2-2-2-2000000000000000000000000000000000000−22−22−22−220000
χ212222222-2-2222222-2-222-20000-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20022220000000000000000000000000000000000002−22−2−22−220000
χ222222222-2-2222222-2-222-20000-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2002222000000000000000000000000000000000000−22−222−22−20000
χ2322222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000
χ2422222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52000000000000
χ2522222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−5222222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000000
χ2622222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−5222222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000000
χ2722222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2222221−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-21−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5222-2-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000
χ2822222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2222221−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-21−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000
χ2922222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-22-2-2-2-21−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52221−521+521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000000
χ3022222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-22-2-2-2-21−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52221−521+521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000000
χ3122222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000
χ3222222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52000000000000
χ3322222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+5222222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000000000
χ3422222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+5222222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000000000
χ3522222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2222221+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-21+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5222-2-21+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000
χ3622222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2222221+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-21+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000
χ3722222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-22-2-2-2-21+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52221+521−521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000000000
χ3822222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-22-2-2-2-21+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52221+521−521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000000000
χ3922-22-22222-2-2-2-2222i−2i2i−2i-2-2-2222i2i2i2i−2i−2i−2i−2i22-2-22222-2-2-2-2−2i2i2i2i−2i−2i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ4022-22-22222-2-2-2-222−2i2i−2i2i-2-2-222−2i−2i−2i−2i2i2i2i2i22-2-22222-2-2-2-22i−2i−2i−2i2i2i-2-2-2-222222i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ4122-22-222-2-2-2-2-2-2222i−2i−2i2i200002i2i2i2i−2i−2i−2i−2i22-2-2-2-2-2-2222200−2i−2i2i2i0000000000000000000000000000000000002−2−22i2−i2−i2i20000
χ4222-22-222-2-2-2-2-2-2222i−2i−2i2i200002i2i2i2i−2i−2i−2i−2i22-2-2-2-2-2-2222200−2i−2i2i2i000000000000000000000000000000000000−222−2−i2i2i2−i20000
χ4322-22-222-2-2-2-2-2-222−2i2i2i−2i20000−2i−2i−2i−2i2i2i2i2i22-2-2-2-2-2-22222002i2i−2i−2i0000000000000000000000000000000000002−2−22−i2i2i2−i20000
χ4422-22-222-2-2-2-2-2-222−2i2i2i−2i20000−2i−2i−2i−2i2i2i2i2i22-2-2-2-2-2-22222002i2i−2i−2i000000000000000000000000000000000000−222−2i2−i2−i2i20000
χ4522-22-2−1+52−1−52221−521−521+521+52−1+52−1−522i−2i2i−2i-222-2-2−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+522i−2i−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14−1+52−1+52−1−52−1−521−521−521+521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ142-22i−2i−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−1+52−1+52−1−52−1−521−521−521+521+52000000000000
χ4622-22-2−1+52−1−52221−521−521+521+52−1+52−1−522i−2i2i−2i-222-2-2−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+522i−2i−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14−1+52−1+52−1−52−1−521−521−521+521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14-22−2i2iζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ141−521−521+521+52−1+52−1+52−1−52−1−52000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.