Finite Group DatabasebetaFinite Group Databasebeta| order | 4616 |
| automorphism | Aut(G) order 2658816 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1154 |
| unambiguous semidirect product | C577⋊Q8 |
| Sylow | C577 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D577 |
| commutator, socle, prime radical, cosocle | C2×C577 | C22 |
| Fitting | C4×C577 | C2 |
| hypercenter | C4 | D577 |
| hypocenter | C577 | Q8 |
| LCS | G ▷ C2×C577 ▷ C577 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4616 |
Polycyclic presentation:
2^3,577|a^2=c,b^2=c,b^a=bc,d^b=d^5761157 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3462, Dic5770, Dic8078, … |
| maximal quotient of | Dic3462, Dic5770, Dic8078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4616, 11);