Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of AGL(1,𝔽25) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×AGL(1,𝔽25) |
| unambiguous semidirect product | (C2×#6053)⋊C3 |
| Fitting, socle | C2×C52 ⋊ C3×C8 |
| derived, Sylow | C52 ⋊ C2×C3×C8 |
| Hall | C2×#6053 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽25) |
| commutator, hypocenter | C52 | C2×C3×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52 | C3×C8 |
| prime radical | C2×(C5⋊D5)⋊C3 | C4 |
| cosocle | #1043 | C22×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 50 |
50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 949);