Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | Dic3×D16 |
| Sylow | C3 ⋊ C4×D16 |
174 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 67 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)(7,14)(8,15)(11,12)(13,19)(16,20)(17,18)(21,22,23);(5,6)(7,10)(8,17)(9,13)(11,14)(12,15)(16,19)(18,20);(1,2,3,4)(22,23)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10715758, Dic3×D32, Dic3×SD64, … |
| maximal normal subgroup of | #10715758, Dic3×D32, Dic3×SD64, … |
| maximal quotient of | C3⋊C8×D16, #10707083, #10707166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4036);