Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C47 ⋊ #2674 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C2×#123×C47 | C2 |
| hypercenter | C2×#123 | D47 |
| hypocenter | C47 | #2674 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
562 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=e,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^46,c^b=cg,d^b=de676 conjugacy classes — view the full character table.
| maximal subgroup of | #26423045, #26423049, #26423129, … |
| maximal normal subgroup of | #26423045, #26423049, #26423129, … |
| maximal quotient of | #26143599, #26143655, #26143921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 10791);