Finite Group DatabasebetaFinite Group Databasebeta| order | 1352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C13 |
No aliases for this group.
| Sylow | C132 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C13⋊D13 |
| commutator, socle, prime radical, cosocle | C2×C132 | C22 |
| Fitting | C4×C132 | C2 |
| hypercenter | C4 | C13⋊D13 |
| hypocenter | C132 | Q8 |
| LCS | G ▷ C2×C132 ▷ C132 | |
| UCS | C1 ◁ C2 ◁ C4 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1352 |
Polycyclic presentation:
2^3,13^2|a^2=c,b^2=c,b^a=bc,d^a=d^12,e^a=e^12341 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1352, 32);