Finite Group DatabasebetaFinite Group Databasebeta| order | 18875 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C25 · Schur multiplier (H2) = C5 |
| direct product | C5×#16836851 |
| unambiguous semidirect product | (C151⋊C5)⋊C25 |
| Fitting, socle | C5×C151 ⋊ C25 |
| derived, Sylow | C151 ⋊ C5×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #16836851 |
| commutator, hypocenter | C151 | C5×C25 |
| Frattini | C1 | G |
| Fitting, socle | C5×C151 | C25 |
| prime radical | C5×C151⋊C5 | C5 |
| cosocle | C151⋊C5 | C52 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C5 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 755 |
155 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18875, 17);