Finite Group DatabasebetaFinite Group Databasebeta| order | 36260 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic1295 |
| derived, Hall | C5×C72×C37 ⋊ C4 |
| Hall | C72×C37 ⋊ Dic5 |
| Hall | C5×C72 ⋊ Dic37 |
| Hall | C5×C37 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic185 |
| Sylow | C37 ⋊ C7⋊Dic35 |
| Sylow | C5 ⋊ C7⋊Dic259 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C7⋊D259) |
| commutator, hypocenter | C5×C72×C37 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C5×C72×C37 | C2 |
| LCS | G ▷ C5×C72×C37 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36260 |
Polycyclic presentation:
2,5,7^2,37,2|a^2=f,b^a=b^4,c^a=c^6,d^a=d^6,e^a=e^369068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36260, 37);