Finite Group DatabasebetaFinite Group Databasebeta| order | 3664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C229 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#11745021 |
| commutator, socle | C2×C229 | C2×C4 |
| Fitting | C4×C229 | C4 |
| prime radical | C2×D229 | C4 |
| cosocle | Dic229 | C22 |
| hypercenter | C4 | #11745021 |
| hypocenter | C229 | M16 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C2 ◁ C4 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1832 |
Polycyclic presentation:
2^4,229|a^2=c,c^2=d,b^a=bd,e^a=e^122,e^b=e^228,e^c=e^228238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3664, 50);