Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #64408⋊C16 |
| derived, Sylow | C73 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #10596842 |
| commutator, hypocenter | C73 | C4×C16 |
| Frattini | C4 | C2×#10596842 |
| Fitting | C8×C73 | C8 |
| socle | C2×C73 | C4×C8 |
| prime radical | C2×D73 | C2×C8 |
| cosocle | #11924036 | C22 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C8 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^6,73|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^10,g^b=g^46,g^c=g^27,g^d=g^72,g^e=g^72136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 1642);