Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C29 ⋊ #2932 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D29 |
| commutator, socle | C22×C29 | C23×C4 |
| Fitting, prime radical | C29×#532 | C2 |
| cosocle | C2×C4×C29 | C24 |
| hypercenter | #532 | D29 |
| hypocenter | C29 | #2932 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
484 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^7,29|a^2=f,c^2=f,f^2=g,b^a=be,c^a=cg,d^a=dg,h^a=h^28,d^b=dg,h^c=h^28436 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 13228);