Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#13094070 |
| Fitting | C22×#41×C47 ⋊ C2 |
| Sylow | C47 ⋊ C22×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D47 |
| commutator | C2×C47 | C26 |
| Frattini | C2 | C25×D47 |
| Fitting | C22×#41×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C22×#41 | D47 |
| hypocenter | C47 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
6560 conjugacy classes of subgroups; only the 3221 normal subgroups are shown.
This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
988 conjugacy classes — view the full character table.
| maximal subgroup of | #26215413, #26215417, #26215445, … |
| maximal normal subgroup of | #26215413, #26215417, #26215445, … |
| maximal quotient of | C22×#15689595, C22×#15689597, C22×#15689603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 19312);