Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C47×#336 ⋊ C2 |
| Sylow | C47 ⋊ #1750 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D47 |
| commutator | C22×C47 | C2×C42 |
| Fitting | C47×#336 | C2 |
| socle | C23×C47 | C22×C4 |
| hypercenter | #336 | D47 |
| hypocenter | C47 | #1750 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 121 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=e,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=cg,h^c=h^46976 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1750, C2×#20243153, C4×#15689088, … |
| maximal normal subgroup of | D47×#1750, C2×#20243153, C4×#15689088, … |
| maximal quotient of | #26106765, #26106767, #26106772, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4275);