Finite Group DatabasebetaFinite Group Databasebeta| order | 6250 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #15691103 ⋊ C2 |
| derived | C52⋊C25 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C5⋊(D25⋊C5) |
| commutator, hypocenter | C52⋊C25 | C2×C5 |
| Frattini, socle | C52 | C5×C5⋊D5 |
| Fitting | #15691103 | C2 |
| LCS | G ▷ C52⋊C25 | |
| UCS | C1 ◁ C5 | |
342 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^5|b^5=e,b^a=b^4e^4,d^a=cd^4,e^a=e^4,f^a=e^4f,c^b=ce,d^b=df160 conjugacy classes — view the full character table.
| maximal subgroup of | #72229808, #72229819 |
| maximal normal subgroup of | #72229819 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6250, 178);