Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C29×#322 ⋊ C2 |
| Sylow | C29 ⋊ #1451 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D29 |
| commutator, socle | C22×C29 | C2×C42 |
| Fitting | C29×#322 | C2 |
| prime radical | C22×D29 | C42 |
| cosocle | C42×C29 | C23 |
| hypercenter | #322 | D29 |
| hypocenter | C29 | #1451 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C42 ◁ #322 | |
208 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 105 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=d,b^2=e,d^2=f,e^2=g,b^a=bg,c^a=cf,h^c=h^28616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 2796);