Finite Group DatabasebetaFinite Group Databasebeta| order | 23698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C17⋊D697 |
| unambiguous semidirect product | C41⋊(C17⋊D17) |
| Fitting, socle, derived, Hall | C172×C41 ⋊ C2 |
| Sylow | C172 ⋊ D41 |
| Sylow | C41 ⋊ C17⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C172×C41 | C2 |
| LCS | G ▷ C172×C41 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11849 |
Polycyclic presentation:
2,17^2,41|b^a=b^16,c^a=c^16,d^a=d^405926 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23698, 10);