Finite Group DatabasebetaFinite Group Databasebeta| order | 24876 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×(C691⋊C3)⋊C4 |
| unambiguous semidirect product | (C691⋊C3)⋊(C3×C4) |
| unambiguous semidirect product | Dic691⋊C32 |
| unambiguous semidirect product | (C3×Dic691)⋊C3 |
| derived, Sylow | C691 ⋊ C32×C4 |
| Hall | C3×C691⋊C3 ⋊ C4 |
| Hall | Dic691 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D691⋊C3 |
| commutator, hypocenter | C691 | C32×C4 |
| Frattini | C2 | C3×D691⋊C3 |
| Fitting, socle | C2×C3×C691 | C2×C3 |
| prime radical | C2×C3×C691⋊C3 | C2 |
| cosocle | C2×C691 | C2×C32 |
| LCS | G ▷ C691 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8292 |
726 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24876, 17);