Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #1436 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D47 |
| commutator | C22×C47 | C2×C42 |
| Fitting | C22×C4⋊C4×C47 | C2 |
| socle | C24×C47 | C23 |
| hypercenter | C22×C4⋊C4 | D47 |
| hypocenter | C47 | #1436 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
612 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=f,b^2=g,c^2=f,b^a=bd,c^a=ce,h^b=h^46976 conjugacy classes — view the full character table.
| maximal subgroup of | #26103308, #26103310, #26107794, … |
| maximal normal subgroup of | #26103308, #26103310, #26107794, … |
| maximal quotient of | #26104197, #26104202, #26104205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2742);