Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C47×#435 ⋊ C2 |
| Sylow | C47 ⋊ D4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D47 |
| commutator, socle | C22×C47 | C23×C4 |
| Fitting | C47×#435 | C2 |
| hypercenter | #435 | D47 |
| hypocenter | C47 | D4×M16 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ #435 | |
544 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,d^c=dg,h^c=h^46,h^d=h^46694 conjugacy classes — view the full character table.
| maximal subgroup of | D4×M16×D47, C2×#20252121, #27080200, … |
| maximal normal subgroup of | D4×M16×D47, C2×#20252121, #27080200, … |
| maximal quotient of | #26187697, #26187705, #26187713, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13243);