Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#10597123 |
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ C2×#67 |
| Sylow | C3 ⋊ C2×#6038 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×D15 |
| commutator, cosocle | C2×C3×C52 | C23 |
| Frattini | C2 | C2×D5×D15 |
| Fitting, socle | C22×C3×C52 | C22 |
| hypocenter | C3×C52 | C2×D4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C22 | |
280 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
138 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11925419, C2×#14268304, C2×#11925646, … |
| maximal normal subgroup of | C2×#11925419, C2×#11925646, C2×D3×#6038, … |
| maximal quotient of | C2×#14268304, #72231028, C2×#14268265 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 852);