Finite Group DatabasebetaFinite Group Databasebeta| order | 18875 |
| automorphism | ? |
| homology | Abelianization (H1) = C125 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C151 ⋊ C125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C25 | C151⋊C5 |
| commutator, hypocenter | C151 | C125 |
| Fitting, cosocle | C25×C151 | C5 |
| socle, prime radical | C5×C151 | C25 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C25 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18875 |
Polycyclic presentation:
5^3,151|a^5=b,b^5=c,d^a=d^59875 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18875, 6);