Finite Group DatabasebetaFinite Group Databasebeta| order | 8525 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C11×C31 ⋊ C25 |
| Sylow | C31 ⋊ C11⋊C25 |
| Sylow | C11 ⋊ C31⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #13133723 |
| commutator, hypocenter | C11×C31 | C25 |
| Fitting, socle | C5×C11×C31 | C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
5,11,31,5|a^5=d,b^a=b^5,c^a=c^2365 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22555293, #30684712, #30684718, … |
| maximal normal subgroup of | C2×#22555293, #30684712, #30684718, … |
| maximal quotient of | C2×#22555293, C3×#22555293 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8525, 6);