Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#15689151 |
| Sylow | C47 ⋊ C2×#424 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D47 |
| commutator | C22×C47 | C23×C4 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C22×M16×C47 | C2 |
| socle | C23×C47 | C22×C4 |
| hypercenter | C22×M16 | D47 |
| hypocenter | C47 | C2×#424 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ C22×M16 | |
512 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
976 conjugacy classes — view the full character table.
| maximal subgroup of | #26122274, #26122276, #26122281, … |
| maximal normal subgroup of | #26122274, #26122276, #26122281, … |
| maximal quotient of | C2×#20242160, C2×#20242164, C2×#20242169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13070);