Finite Group DatabasebetaFinite Group Databasebeta| order | 14528 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#20300284 |
| Fitting | C22×D4×C227 ⋊ C2 |
| Sylow | C227 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D227 |
| commutator, cosocle | C22×C227 | C24 |
| Frattini | C22 | C23×D227 |
| Fitting | C22×D4×C227 | C2 |
| socle | C23×C227 | C23 |
| hypercenter | C22×D4 | D227 |
| hypocenter | C227 | C2×#127 |
| LCS | G ▷ C22×C227 ▷ C227 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7264 |
2288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44400129, #44400130, #44400132, … |
| maximal normal subgroup of | #44400129, #44400130, #44400132, … |
| maximal quotient of | C2×#28408901, C2×#28408932, C2×#28408933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14528, 1088);