Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×D29×C29⋊C7 |
| Fitting, socle | C2×C292 ⋊ C2×C7 |
| derived, Sylow | C292 ⋊ C22×C7 |
| Hall | C29×C29⋊C7 ⋊ C22 |
| Hall | C2×C29×D29 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D29×C29⋊C7 |
| commutator, cosocle, hypocenter | C292 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C292 | C2×C7 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 812 |
352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 79);