Finite Group DatabasebetaFinite Group Databasebeta| order | 1250 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D25 |
| Fitting, Sylow | C252 ⋊ C2 |
| derived | C25 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D25 |
| commutator, hypocenter | C25 | C2×C25 |
| Frattini, socle | C52 | C5×D5 |
| Fitting | C252 | C2 |
| prime radical | C5×D25 | C5 |
| cosocle | C5×C25 | C2×C5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C25 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 50 |
350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D252, C25×#1035, #72228836 |
| maximal normal subgroup of | D252, C25×#1035, #72228836 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1250, 17);