Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
| direct product | C2×#4512 |
| Sylow | C3 ⋊ C2×#347 |
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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 — 3 generators on 21 points:
(3,4,5)(6,7,8,13,9,11,15,18,10,12,14,19,16,17,21,20);(4,5)(7,11,12,17)(8,14)(13,20,19,18)(15,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#347, C4×#4512, #10710016, … |
| maximal normal subgroup of | Dic3×#347, C4×#4512, #10710016, … |
| maximal quotient of | C2×#67511, C2×#67512, #10704187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4000);