Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C29 ⋊ #1311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4×C8 | C2×D29 |
| commutator | C2×C29 | C82 |
| Fitting | C82×C29 | C2 |
| socle, prime radical | C22×C29 | C4×C8 |
| cosocle | C4×C8×C29 | C22 |
| hypercenter | C82 | D29 |
| hypocenter | C29 | #1311 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C4×C8 ◁ C82 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3712 |
Polycyclic presentation:
2^7,29|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=bg,h^a=h^28976 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 2427);