Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C47 ⋊ Q8×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D47 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#477 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #477 | D47 |
| hypocenter | C47 | Q8×Q16 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #477 | |
336 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 133 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=eg,b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,f^c=fg,h^d=h^46472 conjugacy classes — view the full character table.
| maximal subgroup of | #26206430, #26206433, #26206438, … |
| maximal normal subgroup of | #26206430, #26206433, #26206438, … |
| maximal quotient of | #26232880, #26232884, #26234704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 17391);