Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C47 ⋊ C2 |
| Sylow | C47 ⋊ #3496 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C2×H(5,𝔽2)×C47 | C2 |
| hypercenter | C2×H(5,𝔽2) | D47 |
| hypocenter | C47 | #3496 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
1660 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|c^2=g,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^46826 conjugacy classes — view the full character table.
| maximal subgroup of | #26251470, #26251472, #26251488, … |
| maximal normal subgroup of | #26251470, #26251472, #26251488, … |
| maximal quotient of | #26376364, #26376624, #26376636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 18269);