Finite Group DatabasebetaFinite Group Databasebeta| order | 37926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72×C9 · Schur multiplier (H2) = C7 |
| direct product | C2×C72×C43⋊C9 |
| derived, Sylow | C43 ⋊ C2×C72×C9 |
| Hall | C2×C72×C43 ⋊ C9 |
| Hall | C72×C43 ⋊ C2×C9 |
| Hall | C2×C43 ⋊ C72×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C72 | C43⋊C3 |
| commutator, hypocenter | C43 | C2×C72×C9 |
| Frattini | C3 | C2×C72×C43⋊C3 |
| Fitting, socle, prime radical | C2×C3×C72×C43 | C3 |
| cosocle | C3×C43 | C2×C3×C72 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C3×C72 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37926 |
4998 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37926, 177);