Finite Group DatabasebetaFinite Group Databasebeta| order | 36356 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×#10597010 |
| Fitting, socle, Hall | C61×C149 ⋊ C4 |
| derived, Sylow | C149 ⋊ C4×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | #10597010 |
| commutator, hypocenter | C149 | C4×C61 |
| Frattini | C1 | G |
| Fitting, socle | C61×C149 | C4 |
| prime radical | C61×D149 | C2 |
| cosocle | D149 | C2×C61 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C61 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9089 |
2501 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36356, 6);