Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C47 ⋊ #1780 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D47 |
| commutator, socle | C23×C47 | C22×C4 |
| Fitting | C22×#41×C47 | C2 |
| hypercenter | C22×#41 | D47 |
| hypocenter | C47 | #1780 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
612 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=f,f^2=g,b^a=bd,c^a=ce,h^a=h^46,c^b=cg964 conjugacy classes — view the full character table.
| maximal subgroup of | #26103552, #26103554, #26103560, … |
| maximal normal subgroup of | #26103552, #26103554, #26103560, … |
| maximal quotient of | #26107626, #26107629, #26107632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4422);