Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C43 · Schur multiplier (H2) = C2 |
| direct product | C43×#64423⋊C2 |
| unambiguous semidirect product | #64423⋊(C2×C43) |
| unambiguous semidirect product | #64424⋊(C2×C43) |
| Fitting, socle, Hall | C72×C43 ⋊ C22×C3 |
| derived, Sylow | C72 ⋊ C22×C3×C43 |
| Hall | D72×C43 ⋊ C3 |
| Hall | C43×#3861 ⋊ C22 |
| Hall | D72 ⋊ C3×C43 |
| Hall | #3861 ⋊ C22×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #64423⋊C2 |
| commutator, cosocle, hypocenter | C72 | C22×C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C72×C43 | C22×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C43 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 602 |
817 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 265);