Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C47 ⋊ #3028 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#13093993 |
| commutator | C23×C47 | C24 |
| Frattini | C23 | C23×D47 |
| Fitting | C47×#585 | C2 |
| socle | C2×C47 | C2×#120 |
| hypercenter | #585 | D47 |
| hypocenter | C47 | #3028 |
| LCS | G ▷ C23×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #585 | |
716 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=g,d^2=g,b^a=be,c^a=cf,d^a=dg,h^a=h^46,f^b=fg,e^c=eg811 conjugacy classes — view the full character table.
| maximal subgroup of | #26135268, #26135269, #26135272, … |
| maximal normal subgroup of | #26135268, #26135269, #26135272, … |
| maximal quotient of | #26190317, #26190324, #26190331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13916);