Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C29 ⋊ #2330 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D29 |
| commutator | C22×C29 | C23×C4 |
| Fitting | C29×#384 | C2 |
| socle, prime radical, cosocle | C23×C29 | C24 |
| hypercenter | #384 | D29 |
| hypocenter | C29 | #2330 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #384 | |
444 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3712 |
Polycyclic presentation:
2^7,29|a^2=g,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^28436 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 7249);