Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | Dic3×M32 |
| Sylow | C3 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(6,10)(11,16)(12,17)(18,20)(21,22,23);(5,6,7,11,8,12,13,18,9,10,14,16,15,17,19,20);(1,2,3,4)(22,23)120 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#347, #10710016, #10710194, … |
| maximal normal subgroup of | Dic3×#347, #10710016, #10710194, … |
| maximal quotient of | C3⋊C8×M32, #10704181, #10704211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3994);