Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#5243 |
| Sylow | C3 ⋊ C2×#458 |
794 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(7,12)(9,16)(11,17)(13,20)(15,21)(18,19);(1,2)(7,11)(8,14)(12,17)(13,19)(15,21)(18,20);(1,2)(4,5)(6,7,10,13)(8,12,14,20)(9,11,16,19)(15,18,21,17);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10712451, #10712457, #10712465, … |
| maximal normal subgroup of | #10712451, #10712457, #10712465, … |
| maximal quotient of | C2×#71843, C2×#71844, C2×#71890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16684);