Finite Group DatabasebetaFinite Group Databasebeta| order | 1352 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C22×C13×D13 |
| unambiguous semidirect product | C13⋊(C23×C13) |
| unambiguous semidirect product | (C2×C13)⋊(C22×C13) |
| Fitting, socle | C22×C132 ⋊ C2 |
| derived | C13 ⋊ C23×C13 |
| Sylow | C132 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C13 | D13 |
| commutator, cosocle, hypocenter | C13 | C23×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C132 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C13 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#11759817, C22×D132, C13×C22⋊#261, … |
| maximal normal subgroup of | C22×#11759817, C22×D132, C13×C22⋊#261, … |
| maximal quotient of | C2×C13×C22⋊D13, C13×#6129, C13×#6127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1352, 50);