Finite Group DatabasebetaFinite Group Databasebeta| order | 1752 |
| isoclinism | isoclinic class of #64408⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#64408⋊C3 |
| unambiguous semidirect product | #64408⋊(C2×C3) |
| unambiguous semidirect product | (D73⋊C3)⋊C4 |
| unambiguous semidirect product | (C2×#64408)⋊C3 |
| Fitting, socle | C2×C73 ⋊ C3×C4 |
| derived, Sylow | C73 ⋊ C2×C3×C4 |
| Hall | C2×#64408 ⋊ C3 |
| Hall | C73⋊C3 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #64408⋊C3 |
| commutator, hypocenter | C73 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C73 | C3×C4 |
| prime radical | C2×D73⋊C3 | C2 |
| cosocle | D73 | C22×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 146 |
36 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10596842⋊C3, C2×#14581496, D3×#64408⋊C3 |
| maximal normal subgroup of | C2×#10596842⋊C3, C2×#14581496 |
| maximal quotient of | D3×#64408⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1752, 46);