Finite Group DatabasebetaFinite Group Databasebeta| order | 3664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C229 ⋊ C2 |
| Sylow | C229 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D229 |
| commutator, socle, cosocle | C2×C229 | C23 |
| Frattini | C2 | C22×D229 |
| Fitting | C2×C4×C229 | C2 |
| hypercenter | C2×C4 | D229 |
| hypocenter | C229 | #41 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1832 |
Polycyclic presentation:
2^4,229|c^2=d,b^a=bd,e^b=e^228922 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3664, 40);