Finite Group DatabasebetaFinite Group Databasebeta| order | 3875 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C52 |
| unambiguous semidirect product | C52⋊ΓL(1,𝔽32) |
| unambiguous semidirect product | C31⋊H(3,𝔽5) |
| unambiguous semidirect product | (C5×ΓL(1,𝔽32))⋊C5 |
| Fitting | C52×C31 ⋊ C5 |
| Sylow | C31 ⋊ H(3,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C5 | C5×ΓL(1,𝔽32) |
| commutator, socle, cosocle | C5×C31 | C52 |
| Fitting | C52×C31 | C5 |
| hypercenter | C52 | ΓL(1,𝔽32) |
| hypocenter | C31 | H(3,𝔽5) |
| LCS | G ▷ C5×C31 ▷ C31 | |
| UCS | C1 ◁ C5 ◁ C52 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 775 |
Polycyclic presentation:
5^3,31|b^a=bc,d^b=d^16179 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3875, 9);