Finite Group DatabasebetaFinite Group Databasebeta| order | 38125 |
| automorphism | ? |
| homology | Abelianization (H1) = C53 · Schur multiplier (H2) = C52 |
No aliases for this group.
| Sylow | C61 ⋊ #10597837 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C5 | C52×C61⋊C5 |
| commutator, socle, cosocle | C5×C61 | C53 |
| Fitting, prime radical | C61×H(3,𝔽5) | C5 |
| hypercenter | H(3,𝔽5) | C61⋊C5 |
| hypocenter | C61 | #10597837 |
| LCS | G ▷ C5×C61 ▷ C61 | |
| UCS | C1 ◁ C5 ◁ H(3,𝔽5) | |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7625 |
Polycyclic presentation:
5^4,61|c^5=d,b^a=bd,e^c=e^9493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38125, 56);