Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #2310 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C23×Q8×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C23×Q8 | D47 |
| hypocenter | C47 | #2310 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
784 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 309 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,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^46,c^b=ce964 conjugacy classes — view the full character table.
| maximal subgroup of | #26109798, #26109801, #26114010, … |
| maximal normal subgroup of | #26109798, #26109801, #26114010, … |
| maximal quotient of | #26137524, #26137594, #26137668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7096);