Finite Group DatabasebetaFinite Group Databasebeta| order | 36260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| unambiguous semidirect product | D185⋊(C7⋊D7) |
| Fitting, socle, derived, Hall | C5×C72×C37 ⋊ C22 |
| Hall | C72×C37 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D37 |
| Hall | C5×C37 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ D5×D37 |
| Sylow | C37 ⋊ D5×C7⋊D7 |
| Sylow | C5 ⋊ D37×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C37 | C22 |
| LCS | G ▷ C5×C72×C37 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9065 |
Polycyclic presentation:
2^2,5,7^2,37|d^a=d^6,e^a=e^6,f^a=f^36,c^b=c^4,d^b=d^6,e^b=e^62336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36260, 99);