Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×D52 |
| unambiguous semidirect product | (C5×D3×D5)⋊C22 |
| unambiguous semidirect product | (D3×C5⋊D5)⋊C22 |
| unambiguous semidirect product | (D5×D15)⋊C22 |
| Fitting, socle | C2×C3×C52 ⋊ C23 |
| derived, Hall | C3×C52 ⋊ C24 |
| Sylow | C52 ⋊ C23×D3 |
| Sylow | C3 ⋊ C22×D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D52 |
| commutator, cosocle, hypocenter | C3×C52 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52 | C23 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
600 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D52, C2×#14268487, C2×D3×D5⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | C2×D3×D5⋊AGL(1,𝔽5), D3×#87886, D3×#87831, … |
| maximal quotient of | D32×D52, C2×#14268487, D3×#87886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1006);