Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C29 |
| direct product | C2×C7⋊(C29⋊D29) |
| unambiguous semidirect product | (C2×C7)⋊(C29⋊D29) |
| unambiguous semidirect product | (C2×C29)⋊D203 |
| Fitting, socle | C2×C7×C292 ⋊ C2 |
| derived, Hall | C7×C292 ⋊ C22 |
| Sylow | C292 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×C29⋊D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊(C29⋊D29) |
| commutator, cosocle, hypocenter | C7×C292 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C292 | C2 |
| LCS | G ▷ C7×C292 | |
| UCS | C1 ◁ C2 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11774 |
5890 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 112);