Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C47×#399 ⋊ C2 |
| Sylow | C47 ⋊ #2658 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C47×#399 | C2 |
| hypercenter | #399 | D47 |
| hypocenter | C47 | #2658 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #399 | |
612 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 153 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=ef,b^2=eg,d^2=e,b^a=be,c^a=cf,c^b=cg,d^c=de,h^d=h^46538 conjugacy classes — view the full character table.
| maximal subgroup of | #26191462, #26191464, #26191480, … |
| maximal normal subgroup of | #26191462, #26191464, #26191480, … |
| maximal quotient of | #26142803, #26142809, #26143288, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 10619);