Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #1286 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C47⋊#95 |
| commutator | C2×C4×C47 | C42 |
| Frattini | C2×C42 | C2×D47 |
| Fitting | C47×#382 | C2 |
| socle | C22×C47 | #95 |
| hypercenter | #382 | D47 |
| hypocenter | C47 | #1286 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #382 | |
156 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 73 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,c^2=fg,e^2=f,b^a=bc,c^a=cf,e^a=efg,d^b=dg,h^b=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1286, C2×#20241246, #26106056, … |
| maximal normal subgroup of | D47×#1286, C2×#20241246, #26106056, … |
| maximal quotient of | #26102811, #26102820, #26102828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2368);