Finite Group DatabasebetaFinite Group Databasebeta| order | 3664 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C229 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #11745021 |
| commutator, hypocenter | C229 | C16 |
| Fitting | C4×C229 | C4 |
| socle, prime radical | C2×C229 | C8 |
| cosocle | #14270080 | C2 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C4 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 245 |
| transitive degree | μt(G) = 3664 |
Polycyclic presentation:
2^4,229|a^2=b,b^2=c,c^2=d,e^a=e^122,e^b=e^228244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3664, 43);