Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | C47⋊#1273 |
| Sylow | C47 ⋊ #1273 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C42 | C2×D47 |
| commutator | C2×C47 | C82 |
| Fitting | C2×C4×C8×C47 | C2 |
| socle | C23×C47 | C42 |
| hypercenter | C2×C4×C8 | D47 |
| hypocenter | C47 | #1273 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C42 ◁ C2×C4×C8 | |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,h^b=h^461552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26103050, #26103051, #26103063, … |
| maximal normal subgroup of | #26103050, #26103051, #26103063, … |
| maximal quotient of | C47⋊#7014, #26102805, #26102806, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2337);