Finite Group DatabasebetaFinite Group Databasebeta| order | 36084 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×#22583233 |
| Fitting, Hall | C4×C31×C97 ⋊ C3 |
| derived, Hall | C31×C97 ⋊ C3×C4 |
| Hall | C4×C97 ⋊ C31⋊C3 |
| Hall | C4×C31 ⋊ C97⋊C3 |
| Sylow | C97 ⋊ C4×C31⋊C3 |
| Sylow | C31 ⋊ C4×C97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #22583233 |
| commutator, hypocenter | C31×C97 | C3×C4 |
| Frattini | C2 | C2×#22583233 |
| Fitting | C4×C31×C97 | C3 |
| socle, cosocle | C2×C31×C97 | C2×C3 |
| prime radical | C2×#22583233 | C2 |
| LCS | G ▷ C31×C97 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12028 |
4020 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36084, 5);