Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×Dic29⋊C7 |
| unambiguous semidirect product | Dic29⋊(C7×C29) |
| derived | C29 ⋊ C4×C7×C29 |
| Hall | C29×C29⋊C7 ⋊ C4 |
| Hall | C29×Dic29 ⋊ C7 |
| Sylow | C292 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D29⋊C7 |
| commutator, hypocenter | C29 | C4×C7×C29 |
| Frattini | C2 | C29×D29⋊C7 |
| Fitting, socle | C2×C292 | C2×C7 |
| prime radical | C2×C29×C29⋊C7 | C2 |
| cosocle | C2×C29 | C2×C7×C29 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C29 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 812 |
928 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 19);