Finite Group DatabasebetaFinite Group Databasebeta| order | 21386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C17 |
| direct product | C37×C17⋊D17 |
| unambiguous semidirect product | C17⋊(D17×C37) |
| Fitting, socle, Hall | C172×C37 ⋊ C2 |
| derived, Sylow | C172 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C17⋊D17 |
| commutator, cosocle, hypocenter | C172 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C172×C37 | C2 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C37 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10693 |
5402 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21386, 9);