Finite Group DatabasebetaFinite Group Databasebeta| order | 4900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| unambiguous semidirect product | (C5⋊D5)⋊(C7⋊D7) |
| Fitting, socle, derived, Hall | C52×C72 ⋊ C22 |
| Sylow | C72 ⋊ D52 |
| Sylow | C52 ⋊ C2×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C72 | C22 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,7^2|c^a=c^4,e^a=e^6,f^a=f^6,c^b=c^4,d^b=d^4352 conjugacy classes — view the full character table.
| maximal subgroup of | #28413313, #28413315, #28413328, … |
| maximal normal subgroup of | #28413313, #28413315, #28413328, … |
| maximal quotient of | C3×(C5⋊D5)⋊(C7⋊D7), #28413548, #28413555 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4900, 102);