Finite Group DatabasebetaFinite Group Databasebeta| order | 37926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#27162406 |
| Fitting, socle | C3×C72×C43 ⋊ C2×C3 |
| derived, Hall | C72×C43 ⋊ C2×C32 |
| Hall | C3×#20263479 ⋊ C2 |
| Hall | C43×C7⋊D7 ⋊ C32 |
| Hall | C7⋊D7 ⋊ C3×C43⋊C3 |
| Sylow | C72 ⋊ C2×C3×C43⋊C3 |
| Sylow | C43 ⋊ C3×#64424 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #27162406 |
| commutator, cosocle, hypocenter | C72×C43 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C43 | C2×C3 |
| LCS | G ▷ C72×C43 | |
| UCS | C1 ◁ C3 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6321 |
1134 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37926, 340);