Finite Group DatabasebetaFinite Group Databasebeta| order | 37926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×#11725071 |
| derived, Hall | #89205 ⋊ C2×C43 |
| Hall | C43×#89205 ⋊ C2 |
| Hall | C72×C43 ⋊ D9 |
| Sylow | C72 ⋊ D9×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #11725071 |
| commutator, cosocle, hypocenter | #89205 | C2×C43 |
| Frattini | C3 | C43×#64418 |
| Fitting, socle | C3×C72×C43 | D3 |
| LCS | G ▷ #89205 | |
| UCS | C1 ◁ C43 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2709 |
1677 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37926, 167);