Finite Group DatabasebetaFinite Group Databasebeta| order | 6250 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C25 · Schur multiplier (H2) = C1 |
| direct product | C2×#15691084 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | C25⋊C25 |
| commutator | C25 | C2×C5×C25 |
| Frattini | C5×C25 | C2×C52 |
| LCS | G ▷ C25 ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C5×C25 ◁ G | |
56 conjugacy classes of subgroups.
298 conjugacy classes — view the full character table.
| Fitting subgroup of | C2×#15691084⋊C2, C2×#72229807 |
| maximal subgroup of | C2×#15691084⋊C2 |
| maximal normal subgroup of | C2×#15691084⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6250, 27);