Finite Group DatabasebetaFinite Group Databasebeta| order | 3712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C29×#131 ⋊ C4 |
| Sylow | C29 ⋊ #2875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#1181 |
| commutator, socle | C2×C29 | C22×C42 |
| Fitting | C29×#131 | C4 |
| prime radical | #41×D29 | C22 |
| cosocle | C4×D29 | C24 |
| hypercenter | #131 | #1181 |
| hypocenter | C29 | #2875 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C4 ◁ #131 | |
556 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^7,29|a^2=e,b^2=f,e^2=g,b^a=bg,h^b=h^12,d^c=dg,h^f=h^28208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3712, 21080);