Finite Group DatabasebetaFinite Group Databasebeta| order | 36972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| derived | C3×C79 ⋊ C3×C4×C13 |
| Hall | C3×(C79⋊C3)⋊C13 ⋊ C4 |
| Hall | C3⋊((C79⋊C3)⋊C4) ⋊ C13 |
| Hall | C79⋊C13 ⋊ C3×Dic3 |
| Hall | C3×C79⋊C3 ⋊ C4×C13 |
| Sylow | C79 ⋊ C3×Dic3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊AGL(1,𝔽79) |
| commutator, hypocenter | C3×C79 | C3×C4×C13 |
| Fitting, socle, cosocle | C2×C3×C79 | C2×C3×C13 |
| prime radical | C2×C3×(C79⋊C3)⋊C13 | C2 |
| LCS | G ▷ C3×C79 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 948 |
Polycyclic presentation:
2,3,13,3,79,2|a^2=f,d^a=d^2,e^a=e^78,e^b=e^23,e^c=e^18240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36972, 94);