Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D4×D25 |
| Fitting | C3×D4×C25 ⋊ C2 |
| Hall | C3×C25 ⋊ C2×D4 |
| Sylow | C25 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C22×D25 |
| commutator, cosocle | C2×C25 | C23×C3 |
| Frattini | C2×C5 | C22×C3×D5 |
| Fitting | C3×D4×C25 | C2 |
| socle | C2×C3×C5 | C22×D5 |
| hypercenter | C3×D4 | D25 |
| hypocenter | C25 | C2×C3×D4 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C2×C3 ◁ C3×D4 | |
162 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 300 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 153);