Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×#10597114 |
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ C2×#67 |
| Sylow | C3 ⋊ C2×C22⋊(C5⋊D5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×C5⋊D5 |
| commutator, cosocle | C2×C3×C52 | C23 |
| Frattini | C2 | C2×D3×C5⋊D5 |
| Fitting, socle | C22×C3×C52 | C22 |
| hypocenter | C3×C52 | C2×D4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C22 | |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×C22⋊(C5⋊D5), C2×#67×C5⋊D5, C2×#11925606, … |
| maximal normal subgroup of | C2×D3×C22⋊(C5⋊D5), C2×#67×C5⋊D5, C2×#11925606, … |
| maximal quotient of | C2×#14268256, #72230998, #72231354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 823);