Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C29 ⋊ #2183 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D29 |
| commutator, socle, prime radical | C22×C29 | C22×C8 |
| Fitting | C8×Q8×C29 | C2 |
| cosocle | C2×C8×C29 | C23 |
| hypercenter | C8×Q8 | D29 |
| hypocenter | C29 | #2183 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C2×C8 ◁ C8×Q8 | |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3712 |
Polycyclic presentation:
2^7,29|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^28,h^c=h^28616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 6419);