Finite Group DatabasebetaFinite Group Databasebeta| order | 36972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C79⋊C9)⋊#261 |
| derived, Hall | C13×C79 ⋊ C4×C9 |
| Hall | C13×C79⋊C9 ⋊ C4 |
| Hall | C79⋊#261 ⋊ C9 |
| Hall | C79⋊C9 ⋊ #261 |
| Sylow | C79 ⋊ C9×#261 |
| Sylow | C13 ⋊ Dic79⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C79⋊C3)⋊#261 |
| commutator, hypocenter | C13×C79 | C4×C9 |
| Fitting, socle | C3×C13×C79 | C3×C4 |
| prime radical, cosocle | C3×D13×C79 | C2×C3 |
| LCS | G ▷ C13×C79 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9243 |
Polycyclic presentation:
2,3,2,13,79,3|a^2=c,b^3=f,d^a=d^5,e^a=e^78,e^b=e^23,d^c=d^12375 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36972, 50);