Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4×C5 |
| direct product | C4×C3⋊#1039 |
| derived, Hall | C3×C52 ⋊ C42 |
| Sylow | C52 ⋊ C4×Dic3 |
| Sylow | C3 ⋊ C4×#1039 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C3⋊(C5⋊D5) |
| commutator, hypocenter | C3×C52 | C42 |
| Frattini | C22 | C2×C3⋊(C5⋊D5) |
| Fitting | C2×C3×C4×C52 | C2 |
| socle, prime radical, cosocle | C22×C3×C52 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2×C4 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1200 |
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×Dic3×C5⋊D5, C4×D3×#1039, C42×C3⋊(C5⋊D5), … |
| maximal normal subgroup of | C4×Dic3×C5⋊D5, C4×D3×#1039, C42×C3⋊(C5⋊D5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 456);