Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C47 ⋊ C4×C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D47 |
| commutator | C2×C47 | C2×C4×C8 |
| Fitting | C47×#336 | C2 |
| socle | C23×C47 | C22×C4 |
| hypercenter | #336 | D47 |
| hypocenter | C47 | C4×C4⋊C8 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
316 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 161 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=de,f^2=g,b^a=bd,h^c=h^461000 conjugacy classes — view the full character table.
| maximal subgroup of | #26104214, #26104216, #26104222, … |
| maximal normal subgroup of | #26104214, #26104216, #26104222, … |
| maximal quotient of | #26107398, #26107402, #26107411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4358);