Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | C4×D3×C5⋊D5 |
| Fitting | C3×C4×C52 ⋊ C22 |
| derived, Hall | C3×C52 ⋊ C22×C4 |
| Sylow | C52 ⋊ C2×C4×D3 |
| Sylow | C3 ⋊ C2×C4×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×C5⋊D5 |
| commutator, hypocenter | C3×C52 | C22×C4 |
| Frattini | C2 | C2×D3×C5⋊D5 |
| Fitting | C3×C4×C52 | C22 |
| socle, cosocle | C2×C3×C52 | C23 |
| prime radical | C2×D3×C5⋊D5 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C4 | |
432 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 300 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×D3×C5⋊D5, C4×D3×#1043, D3×D4×C5⋊D5, … |
| maximal normal subgroup of | C2×C4×D3×C5⋊D5, C4×D3×#1043, D3×D4×C5⋊D5, … |
| maximal quotient of | C2×C4×D3×C5⋊D5, C4×Dic3×C5⋊D5, C5⋊D5×#624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 813);