Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C29 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #1181 |
| commutator, hypocenter | C29 | C4×C32 |
| Frattini | C2×C8 | C2×#1181 |
| Fitting | C2×C16×C29 | C4 |
| socle, prime radical | C22×C29 | C2×C16 |
| cosocle | C2×#90768 | C22 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C16 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3712 |
Polycyclic presentation:
2^7,29|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,h^a=h^12,h^b=h^28,h^c=h^28352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 19615);