Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C49 · Schur multiplier (H2) = C2 |
| derived, Hall | C3×C43 ⋊ C22×C49 |
| Hall | C3×C43⋊C49 ⋊ C22 |
| Hall | C43⋊C49 ⋊ C2×D3 |
| Hall | D3×D43 ⋊ C49 |
| Sylow | C43 ⋊ C2×D3×C49 |
| Sylow | C3 ⋊ C2×D43⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | D3×D43⋊C7 |
| commutator, hypocenter | C3×C43 | C22×C49 |
| Fitting, socle, cosocle | C3×C7×C43 | C22×C7 |
| prime radical | D3×C7×D43 | C7 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 ◁ C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6321 |
357 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 33);