Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | #66524⋊(C7⋊D7) |
| derived, Hall | C72×C37 ⋊ C2×C9 |
| Hall | C72×#66524 ⋊ C2 |
| Hall | C7⋊D259 ⋊ C9 |
| Hall | #66524 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ #66524⋊C2 |
| Sylow | C37 ⋊ C9×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C37⋊C3)⋊(C7⋊D7) |
| commutator, hypocenter | C72×C37 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C37 | C2×C3 |
| prime radical | C3×C7⋊D259 | C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16317 |
Polycyclic presentation:
2,3,7^2,37,3|b^3=f,c^a=c^6,d^a=d^6,e^a=e^36,e^b=e^261116 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 137);