Finite Group DatabasebetaFinite Group Databasebeta| order | 1352 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#1057 |
| derived | C13 ⋊ C8×C13 |
| Sylow | C132 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | #261 |
| commutator, hypocenter | C13 | C8×C13 |
| Frattini | C2 | C13×#261 |
| Fitting, socle, prime radical | C2×C132 | C4 |
| cosocle | Dic13 | C2×C13 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C13 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | #72229225, #72229229, C13×#6122, … |
| maximal normal subgroup of | #72229225, #72229229, C13×#6122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1352, 18);