Finite Group DatabasebetaFinite Group Databasebeta| order | 1250 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #10597832 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C5 | (C5⋊D5)⋊C5 |
| commutator, cosocle, hypocenter | H(3,𝔽5) | C2×C5 |
| Frattini | C52 | C5×D5 |
| Fitting | #10597832 | C2 |
| prime radical | #6953 | C5 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 125 |
Polycyclic presentation:
2,5^4|c^5=e,b^a=b^4,d^a=d^4e,c^b=cd,d^b=de62 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1250, 32);