Finite Group DatabasebetaFinite Group Databasebeta| order | 14528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C227 ⋊ C2 |
| Sylow | C227 ⋊ #510 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7264 |
Polycyclic presentation:
2^6,227|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^226,d^b=de,e^b=ef,g^b=g^2262276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44401624, #44401627, #44401686, … |
| maximal normal subgroup of | #44401624, #44401627, #44401686, … |
| maximal quotient of | #44401447, #44401455, #44401522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14528, 992);