Finite Group DatabasebetaFinite Group Databasebeta| order | 36972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| derived, Hall | C13×C79 ⋊ C32×C4 |
| Hall | C13⋊C3×C79⋊C3 ⋊ C4 |
| Hall | C13×Dic79 ⋊ C32 |
| Hall | Dic79 ⋊ C3×C13⋊C3 |
| Sylow | C79 ⋊ C3×C4×C13⋊C3 |
| Sylow | C13 ⋊ C3×(C79⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C13⋊C3×D79⋊C3 |
| commutator, hypocenter | C13×C79 | C32×C4 |
| Fitting, socle, cosocle | C2×C13×C79 | C2×C32 |
| prime radical | C2×C13⋊C3×C79⋊C3 | C2 |
| LCS | G ▷ C13×C79 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4108 |
266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36972, 104);