Finite Group DatabasebetaFinite Group Databasebeta| order | 3664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic229 |
| Sylow | C229 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D229 |
| commutator | C2×C229 | C2×C4 |
| Fitting | C2×C4×C229 | C2 |
| socle, prime radical, cosocle | C22×C229 | C22 |
| hypercenter | C2×C4 | D229 |
| hypocenter | C229 | C4⋊C4 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3664 |
Polycyclic presentation:
2^4,229|a^2=d,b^2=c,b^a=bc,e^a=e^228922 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3664, 20);