Finite Group DatabasebetaFinite Group Databasebeta| order | 23198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1657 |
| unambiguous semidirect product | C1657⋊(C2×C7) |
| Fitting, socle, Hall | C7×C1657 ⋊ C2 |
| derived, Sylow | C1657 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1657 |
| commutator, cosocle, hypocenter | C1657 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C1657 | C2 |
| LCS | G ▷ C1657 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11599 |
5810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23198, 2);