Finite Group DatabasebetaFinite Group Databasebeta| order | 23698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C41 · Schur multiplier (H2) = C1 |
| direct product | C17×D17×C41 |
| unambiguous semidirect product | C17⋊(C2×C17×C41) |
| Fitting, socle, Hall | C172×C41 ⋊ C2 |
| derived | C17 ⋊ C2×C17×C41 |
| Sylow | C172 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C41 | D17 |
| commutator, cosocle, hypocenter | C17 | C2×C17×C41 |
| Frattini | C1 | G |
| Fitting, socle | C172×C41 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C17×C41 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1394 |
6970 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23698, 7);