Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #2153 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×D188 |
| commutator | C4×C47 | C22×C8 |
| Frattini | C2×C8 | C22×D47 |
| Fitting | C47×#405 | C2 |
| socle | C2×C47 | C2×C4⋊C8 |
| hypercenter | #405 | D47 |
| hypocenter | C47 | #2153 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C8 ◁ C22×C8 ◁ #405 | |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^46,c^b=cg964 conjugacy classes — view the full character table.
| maximal subgroup of | #26127795, #26127796, #26127800, … |
| maximal normal subgroup of | #26127795, #26127796, #26127800, … |
| maximal quotient of | #26127826, #26127852, #26127886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6276);