Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C47×#396 ⋊ C2 |
| Sylow | C47 ⋊ #2643 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C47×#396 | C2 |
| hypercenter | #396 | D47 |
| hypocenter | C47 | #2643 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #396 | |
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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=fg,b^2=f,b^a=be,c^a=cf,h^a=h^46,c^b=cg,d^c=de,h^d=h^46538 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2643, C2×#20249345, #26382802, … |
| maximal normal subgroup of | D47×#2643, C2×#20249345, #26382802, … |
| maximal quotient of | #26142665, #26142709, #26143396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 10467);