Finite Group DatabasebetaFinite Group Databasebeta| order | 3664 |
| isoclinism | isoclinic class of D229 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D229 |
| Fitting | C8×C229 ⋊ C2 |
| derived, Sylow | C229 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D229 |
| commutator, hypocenter | C229 | C2×C8 |
| Frattini | C4 | C2×D229 |
| Fitting | C8×C229 | C2 |
| socle | C2×C229 | C2×C4 |
| prime radical | C2×D229 | C4 |
| cosocle | C4×C229 | C22 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1832 |
928 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3664, 21);