Finite Group DatabasebetaFinite Group Databasebeta| order | 36356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D61×D149 |
| unambiguous semidirect product | (D61×C149)⋊C2 |
| unambiguous semidirect product | (C61×D149)⋊C2 |
| unambiguous semidirect product | D9089⋊C2 |
| Fitting, socle, derived, Hall | C61×C149 ⋊ C22 |
| Sylow | C149 ⋊ C2×D61 |
| Sylow | C61 ⋊ C2×D149 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C61×C149 | C22 |
| LCS | G ▷ C61×C149 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9089 |
2432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36356, 12);