Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C8×C73 ⋊ C8 |
| Sylow | C73 ⋊ #322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#10596842 |
| commutator, socle | C2×C73 | C4×C8 |
| Fitting | C8×C73 | C8 |
| prime radical | C2×D73 | C42 |
| cosocle | C4×#64408 | C22 |
| hypercenter | C8 | #10596842 |
| hypocenter | C73 | #322 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C8 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 584 |
Polycyclic presentation:
2^6,73|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^b=g^10,g^d=g^27,g^f=g^72112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 1633);