Finite Group DatabasebetaFinite Group Databasebeta| order | 37926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C43 · Schur multiplier (H2) = C3 |
| direct product | C3×C43×#64424 |
| Fitting, socle | C3×C72×C43 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C32×C43 |
| Hall | C3×C43×#3861 ⋊ C2 |
| Hall | C43×C7⋊D7 ⋊ C32 |
| Hall | C72×C43 ⋊ C2×C32 |
| Hall | C3×#3861 ⋊ C2×C43 |
| Hall | C7⋊D7 ⋊ C32×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C43 | #64424 |
| commutator, cosocle, hypocenter | C72 | C2×C32×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C43 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C43 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6321 |
1806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37926, 337);