Finite Group DatabasebetaFinite Group Databasebeta| order | 21534 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C97⋊C3)⋊D37 |
| Fitting, socle, derived, Hall | C37×C97 ⋊ C2×C3 |
| Hall | C37×C97⋊C3 ⋊ C2 |
| Hall | D3589 ⋊ C3 |
| Hall | C97⋊C3 ⋊ D37 |
| Sylow | C97 ⋊ C3×D37 |
| Sylow | C37 ⋊ D97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C97 | C2×C3 |
| LCS | G ▷ C37×C97 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3589 |
Polycyclic presentation:
2,3,37,97|c^a=c^36,d^a=d^96,d^b=d^35652 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21534, 21);