Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C47 ⋊ C2 |
| Sylow | C47 ⋊ #2342 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C4×C22⋊C4×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C4×C22⋊C4 | D47 |
| hypocenter | C47 | #2342 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
792 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=g,b^2=f,b^a=be,c^a=cf,d^b=de,h^c=h^46970 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2342, C2×#20246231, #26375547, … |
| maximal normal subgroup of | D47×#2342, C2×#20246231, #26375547, … |
| maximal quotient of | C22⋊C4×(C2×D47)⋊C4, #26137688, #26137712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7353);