Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D109⋊C64 |
| derived, Sylow | C109 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #89137 |
| commutator, hypocenter | C109 | C2×C64 |
| Frattini | C16 | C2×#89137 |
| Fitting | C32×C109 | C4 |
| socle | C2×C109 | C2×C32 |
| prime radical | C2×D109 | C32 |
| cosocle | #16812605 | C22 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C32 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6976 |
Polycyclic presentation:
2^7,109|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^33,h^b=h^108,h^c=h^108992 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 19678);