Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#878 |
| Sylow | C3 ⋊ C22×C22⋊Q8 |
1840 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 685 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 19 points:
(1,2)(3,4)(5,6,7)(8,9)(10,11)(12,15,16,14)(13,17,18,19);(1,2)(3,4)(9,11)(12,14)(13,17)(15,16)(18,19);(6,7)(12,13,16,18)(14,17,15,19);(3,4);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10687816, #10687835, #10704095, … |
| maximal normal subgroup of | #10687816, #10687835, #10704095, … |
| maximal quotient of | C22×#4942, C22×#4946, C22×#4950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18259);