Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C29×C32 ⋊ C4 |
| Sylow | C29 ⋊ #1397 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×#1181 |
| commutator, socle | C2×C29 | C4×C16 |
| Fitting | C29×C32 | C4 |
| prime radical | C2×D29 | C2×C16 |
| cosocle | C16×D29 | C22 |
| hypercenter | C32 | #1181 |
| hypocenter | C29 | #1397 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C16 ◁ C32 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^7,29|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^12,h^d=h^28304 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 19616);