Finite Group DatabasebetaFinite Group Databasebeta| order | 4900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D352 |
| Fitting, socle, derived, Hall | C52×C72 ⋊ C22 |
| Sylow | C72 ⋊ D52 |
| Sylow | C52 ⋊ D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C72 | C22 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
361 conjugacy classes — view the full character table.
| maximal subgroup of | #28413316, #28413318, D35×C5⋊AGL(1,𝔽7), … |
| maximal normal subgroup of | #28413316, #28413318, D35×C5⋊AGL(1,𝔽7), … |
| maximal quotient of | C3×D352, D35×D105, #28413558 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4900, 103);