Finite Group DatabasebetaFinite Group Databasebeta| order | 36905 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C112×C61 ⋊ C5 |
| Sylow | C112 ⋊ C61⋊C5 |
| Sylow | C61 ⋊ #10597244 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C61 | C5 |
| LCS | G ▷ C112×C61 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3355 |
Polycyclic presentation:
5,11^2,61|b^a=b^4,c^a=c^5,d^a=d^201481 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36905, 24);