Finite Group DatabasebetaFinite Group Databasebeta| order | 1250 |
| isoclinism | isoclinic class of #11929376 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, Sylow | H(3,𝔽5)⋊C5 ⋊ C2 |
| derived | C53 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C53 | C2×C5 |
| Frattini | C52 | C5×D5 |
| Fitting | H(3,𝔽5)⋊C5 | C2 |
| socle | C5 | (C5⋊D5)⋊C5 |
| LCS | G ▷ C53 | |
| UCS | C1 | |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 25 |
Polycyclic presentation:
2,5^4|c^a=c^4,d^a=d^4,e^a=e^4,c^b=cd,d^b=de32 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1250, 27);