Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C47⋊#1308 |
| Sylow | C47 ⋊ #1308 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C47⋊#95 |
| commutator | C23×C47 | C42 |
| Frattini | C2×C42 | C2×D47 |
| Fitting | C47×#432 | C2 |
| socle | C22×C47 | #95 |
| hypercenter | #432 | D47 |
| hypocenter | C47 | #1308 |
| LCS | G ▷ C23×C47 ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #432 | |
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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=d,b^2=e,d^2=fg,e^2=f,b^a=bc,c^a=cf,e^a=eg,c^b=cg,d^b=df,h^b=h^46670 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1308, C2×C47⋊#1308, #26106680, … |
| maximal normal subgroup of | D47×#1308, C2×C47⋊#1308, #26106680, … |
| maximal quotient of | #26102850, #26102851, #26102852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2422);