Finite Group DatabasebetaFinite Group Databasebeta| order | 36905 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C61×C121 ⋊ C5 |
| Sylow | C121 ⋊ C61⋊C5 |
| Sylow | C61 ⋊ C121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C61×C121 | C5 |
| Frattini | C11 | #16809821 |
| socle | C11×C61 | C11⋊C5 |
| LCS | G ▷ C61×C121 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7381 |
Polycyclic presentation:
5,11,61,11|b^11=d,b^a=b^3,c^a=c^9,d^a=d^31481 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36905, 4);