Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C109 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #89137 |
| commutator, hypocenter | C109 | C4×C32 |
| Frattini | C2×C8 | C2×#89137 |
| Fitting | C2×C16×C109 | C4 |
| socle, prime radical | C22×C109 | C2×C16 |
| cosocle | C2×#13182004 | C22 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C16 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13952 |
Polycyclic presentation:
2^7,109|a^2=c,b^2=d,c^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, 19615);