Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C73 ⋊ #407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#64408 |
| commutator, socle | C22×C73 | C22×C4 |
| Fitting, prime radical | C24×C73 | C4 |
| cosocle | C2×Dic73 | C23 |
| hypercenter | C24 | #64408 |
| hypocenter | C73 | #407 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C24 | |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^6,73|a^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^27,g^e=g^72316 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 1519);