Finite Group DatabasebetaFinite Group Databasebeta| order | 24860 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊Dic113 |
| unambiguous semidirect product | Dic1243⋊C5 |
| derived, Hall | C11×C113 ⋊ C4×C5 |
| Hall | C11⋊C5×C113 ⋊ C4 |
| Hall | Dic1243 ⋊ C5 |
| Sylow | C113 ⋊ Dic11⋊C5 |
| Hall | C11⋊C5 ⋊ Dic113 |
| Sylow | C11 ⋊ C5×Dic113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C11⋊C5)⋊D113 |
| commutator, hypocenter | C11×C113 | C4×C5 |
| Fitting, socle, cosocle | C2×C11×C113 | C2×C5 |
| prime radical | C2×C11⋊C5×C113 | C2 |
| LCS | G ▷ C11×C113 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4972 |
Polycyclic presentation:
2,5,11,113,2|a^2=e,c^a=c^10,d^a=d^112,c^b=c^4806 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24860, 12);