Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C22⋊(C52⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22×C5 |
| direct product | C22×C22⋊(C52⋊C3) |
| Fitting, socle, Hall | C24×C52 ⋊ C3 |
| derived | C22×C52 ⋊ C22×C3 |
| Sylow | C52 ⋊ C22×A4 |
| Sylow | C24 ⋊ C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C22⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C22×C52 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C52 | C3 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 ◁ C22 | |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C22×(C5⋊D5)⋊A4 |
| maximal normal subgroup of | C22×(C5⋊D5)⋊A4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1032);