Finite Group DatabasebetaFinite Group Databasebeta| order | 4616 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C577 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C577 | C8 |
| prime radical | D577 | C4 |
| cosocle | #14556313 | C2 |
| LCS | G ▷ C577 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 577 |
| transitive degree | μt(G) = 577 |
Polycyclic presentation:
2^3,577|a^2=b,b^2=c,d^a=d^391,d^b=d^553,d^c=d^57680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4616, 15);