Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C47 ⋊ #1440 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D47 |
| commutator | C23×C47 | C22×C4 |
| Fitting | C22×C22⋊C4×C47 | C2 |
| socle | C24×C47 | C23 |
| hypercenter | C22×C22⋊C4 | D47 |
| hypocenter | C47 | #1440 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
736 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=g,c^2=d,b^a=bd,c^a=ce,c^b=cf,h^c=h^46964 conjugacy classes — view the full character table.
| maximal subgroup of | #26108851, D47×#1440, C2×#20241635, … |
| maximal normal subgroup of | #26108851, D47×#1440, C2×#20241635, … |
| maximal quotient of | #26104200, #26104201, #26104203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2757);