Finite Group DatabasebetaFinite Group Databasebeta| order | 36972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived | C3×C79 ⋊ C22×C3×C13 |
| Hall | C3×(C79⋊C3)⋊C13 ⋊ C22 |
| Hall | D3×D79⋊C3 ⋊ C13 |
| Hall | C79⋊C13 ⋊ C2×C3×D3 |
| Hall | C3×C79⋊C3 ⋊ C22×C13 |
| Sylow | C79 ⋊ C2×C3×D3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C79 | C22×C3×C13 |
| LCS | G ▷ C3×C79 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 237 |
237 conjugacy classes — view the full character table.
| holomorph of | C3×C79 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36972, 151);