Finite Group DatabasebetaFinite Group Databasebeta| order | 23244 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×#10597010 |
| unambiguous semidirect product | (C13×#10597010)⋊C3 |
| Fitting, socle, derived, Hall | C13×C149 ⋊ C3×C4 |
| Hall | C13×#10597010 ⋊ C3 |
| Hall | C13⋊C3×C149 ⋊ C4 |
| Sylow | C149 ⋊ C4×C13⋊C3 |
| Sylow | C13 ⋊ C3×#10597010 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C149 | C3×C4 |
| prime radical | C13⋊C3×D149 | C2 |
| cosocle | C13×D149 | C2×C3 |
| LCS | G ▷ C13×C149 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1937 |
287 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23244, 20);