Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C47 ⋊ #1313 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic47 |
| commutator | C4×C47 | C4×C8 |
| Frattini | C4×C8 | C2×D47 |
| Fitting | C47×#346 | C2 |
| socle | C22×C47 | #97 |
| hypercenter | #346 | D47 |
| hypocenter | C47 | #1313 |
| LCS | G ▷ C4×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ #346 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,h^a=h^46,c^b=cg,h^b=h^46964 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1313, C2×#20241310, #26125277, … |
| maximal normal subgroup of | D47×#1313, C2×#20241310, #26125277, … |
| maximal quotient of | #26102895, #26103107, #26103615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2432);