Finite Group DatabasebetaFinite Group Databasebeta| order | 37668 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#34038058 |
| Fitting, socle | C2×C43×C73 ⋊ C2×C3 |
| derived, Hall | C43×C73 ⋊ C22×C3 |
| Hall | C2×D3139 ⋊ C3 |
| Hall | #22627924 ⋊ C22 |
| Sylow | C73 ⋊ C2×D43⋊C3 |
| Sylow | C43 ⋊ C2×D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #34038058 |
| commutator, cosocle, hypocenter | C43×C73 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C43×C73 | C2×C3 |
| LCS | G ▷ C43×C73 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6278 |
1058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37668, 41);