Finite Group DatabasebetaFinite Group Databasebeta| order | 1352 |
| isoclinism | isoclinic class of D132 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D13×Dic13 |
| derived, Sylow | C132 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D132 |
| commutator, hypocenter | C132 | C2×C4 |
| Fitting, socle, cosocle | C2×C132 | C22 |
| prime radical | C2×C13×D13 | C2 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #72229237, C4×D132, #72259216, … |
| maximal normal subgroup of | #72229237, C4×D132, #72259216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1352, 22);