Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #6037 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#6038 |
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D52 |
| commutator, cosocle | C2×C52 | C23×C3 |
| Frattini | C2 | C2×C3×D52 |
| Fitting, socle | C22×C3×C52 | C22 |
| hypocenter | C52 | C2×C3×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22×C3 | |
280 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#87886, C2×C3×#10597127, C2×D3×#6038, … |
| maximal normal subgroup of | C2×C3×#87886, C2×D3×#6038, C2×#11925428, … |
| maximal quotient of | C2×C3×#10597127, C3×#11716943, C2×C32×#6038, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 772);