Finite Group DatabasebetaFinite Group Databasebeta| order | 24252 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊((C43⋊C3)⋊C4) |
| unambiguous semidirect product | (C43⋊C3)⋊Dic47 |
| unambiguous semidirect product | Dic2021⋊C3 |
| derived, Hall | C43×C47 ⋊ C3×C4 |
| Hall | Dic2021 ⋊ C3 |
| Hall | C47×C43⋊C3 ⋊ C4 |
| Hall | C43⋊C3 ⋊ Dic47 |
| Sylow | C47 ⋊ (C43⋊C3)⋊C4 |
| Sylow | C43 ⋊ C3×Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C47⋊(D43⋊C3) |
| commutator, hypocenter | C43×C47 | C3×C4 |
| Fitting, socle, cosocle | C2×C43×C47 | C2×C3 |
| prime radical | C2×C47×C43⋊C3 | C2 |
| LCS | G ▷ C43×C47 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8084 |
Polycyclic presentation:
2,3,43,47,2|a^2=e,c^a=c^42,d^a=d^46,c^b=c^36808 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24252, 12);