Finite Group DatabasebetaFinite Group Databasebeta| order | 36025 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C11×C131 ⋊ C25 |
| Sylow | C131 ⋊ C11⋊C25 |
| Sylow | C11 ⋊ C131⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #20297887 |
| commutator, hypocenter | C11×C131 | C25 |
| Fitting, socle, prime radical, cosocle | C5×C11×C131 | C5 |
| LCS | G ▷ C11×C131 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36025 |
Polycyclic presentation:
5,11,131,5|a^5=d,b^a=b^5,c^a=c^531465 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36025, 6);