Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D5×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D5×D15 |
| Fitting, socle | C22×C3×C52 ⋊ C22 |
| derived, Hall | C3×C52 ⋊ C24 |
| Sylow | C52 ⋊ C23×D3 |
| Sylow | C3 ⋊ C22×D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×D15 |
| commutator, cosocle, hypocenter | C3×C52 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C22 | |
600 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×D52, D15×C22⋊AGL(1,𝔽5), #72230105, … |
| maximal normal subgroup of | C22×D3×D52, D15×C22⋊AGL(1,𝔽5), #72230105, … |
| maximal quotient of | C22×D5×C3⋊D15, #72230616, C22×D152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1028);