Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#908 |
| Fitting | C22×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C22×AGL(1,ℤ/8) |
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 5 generators on 15 points:
(5,6,7)(8,9,10,12,11,13,14,15);(1,2)(3,4)(9,13)(12,15);(6,7)(9,12)(10,14)(13,15);(3,4);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10701915, #10701919, #10701929, … |
| maximal normal subgroup of | #10701915, #10701919, #10701929, … |
| maximal quotient of | C22×#5131, C22×#5133, C22×#5121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19731);