Finite Group DatabasebetaFinite Group Databasebeta| order | 10525 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C5 |
| direct product | C5×C421⋊C5 |
| unambiguous semidirect product | C421⋊C52 |
| unambiguous semidirect product | (C5×C421)⋊C5 |
| Fitting, socle | C5×C421 ⋊ C5 |
| derived, Sylow | C421 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C421⋊C5 |
| commutator, cosocle, hypocenter | C421 | C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C421 | C5 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
445 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D421⋊C5, C5⋊(D421⋊C5), D5×C421⋊C5, … |
| maximal normal subgroup of | C5×D421⋊C5, C5⋊(D421⋊C5), D5×C421⋊C5, … |
| maximal quotient of | C2×C5×C421⋊C5, C3×C5×C421⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10525, 3);