Finite Group DatabasebetaFinite Group Databasebeta| order | 37668 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×#22627924 |
| Fitting, socle, Hall | C22×C43×C73 ⋊ C3 |
| derived, Hall | C43×C73 ⋊ C22×C3 |
| Hall | C22×C73 ⋊ C43⋊C3 |
| Hall | C22×C43 ⋊ C73⋊C3 |
| Sylow | C73 ⋊ C22×C43⋊C3 |
| Sylow | C43 ⋊ C22×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #22627924 |
| commutator, cosocle, hypocenter | C43×C73 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C43×C73 | C3 |
| LCS | G ▷ C43×C73 | |
| UCS | C1 ◁ C22 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12556 |
4196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37668, 69);