Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#27162347 |
| Fitting | C2×C43×C49 ⋊ C2×C3 |
| derived, Hall | C43×C49 ⋊ C22×C3 |
| Hall | C2×C49×D43 ⋊ C3 |
| Hall | #20263466 ⋊ C22 |
| Hall | C2×D43 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ C2×D43⋊C3 |
| Sylow | C43 ⋊ C22×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #27162347 |
| commutator, cosocle, hypocenter | C43×C49 | C22×C3 |
| Frattini | C7 | C2×#14268587 |
| Fitting | C2×C43×C49 | C2×C3 |
| socle | C2×C7×C43 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C43×C49 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4214 |
762 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 53);