Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C29 |
| direct product | C7×#16809858 |
| Fitting, socle, Hall | C7×C292 ⋊ C4 |
| derived, Sylow | C292 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #16809858 |
| commutator, hypocenter | C292 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C292 | C4 |
| prime radical | C7×C29⋊D29 | C2 |
| cosocle | C29⋊D29 | C2×C7 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C7 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 406 |
1498 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 98);