Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #1043⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#1043⋊C3 |
| unambiguous semidirect product | (C4×#1043)⋊C3 |
| Fitting | C4×C52 ⋊ C3×C4 |
| derived, Sylow | C52 ⋊ C3×C42 |
| Hall | C4×#1043 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #1043⋊C3 |
| commutator, hypocenter | C52 | C3×C42 |
| Frattini | C2 | C2×#1043⋊C3 |
| Fitting | C4×C52 | C3×C4 |
| socle | C2×C52 | C2×C3×C4 |
| prime radical | C2×(C5⋊D5)⋊C3 | C22 |
| cosocle | C2×C5⋊D5 | C22×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C4 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×#1043⋊C3, C4×AGL(1,𝔽25), C8×#1043⋊C3, … |
| maximal normal subgroup of | C3×C4×#1043⋊C3, C4×AGL(1,𝔽25), C8×#1043⋊C3, … |
| maximal quotient of | C3×C4×#1043⋊C3, C8×#1043⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 501);