Finite Group DatabasebetaFinite Group Databasebeta| order | 25047 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C23 · Schur multiplier (H2) = C11 |
| direct product | C23×C112⋊C9 |
| unambiguous semidirect product | C112⋊(C9×C23) |
| unambiguous semidirect product | (C112×C23)⋊C9 |
| derived, Sylow | C112 ⋊ C9×C23 |
| Hall | C112×C23 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | C112⋊C3 |
| commutator, hypocenter | C112 | C9×C23 |
| Frattini | C3 | C23×C112⋊C3 |
| Fitting, socle, prime radical | C3×C112×C23 | C3 |
| cosocle | C3×C112 | C3×C23 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C3×C23 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2277 |
2967 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25047, 7);