Finite Group DatabasebetaFinite Group Databasebeta| order | 1352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D169 |
| Fitting | C22×C169 ⋊ C2 |
| Sylow | C169 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D169 |
| commutator, cosocle | C2×C169 | C22 |
| Frattini, socle | C2×C13 | C2×D13 |
| Fitting | C22×C169 | C2 |
| hypercenter | C22 | D169 |
| hypocenter | C169 | D4 |
| LCS | G ▷ C2×C169 ▷ C169 | |
| UCS | C1 ◁ C2 ◁ C22 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 676 |
Polycyclic presentation:
2^3,13^2|d^13=e,b^a=bc,d^a=d^12e^12,e^a=e^12341 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1352, 8);