Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q16×#67 |
| Fitting | C22×C3×Q16 ⋊ C2 |
| Sylow | C3 ⋊ D4×Q16 |
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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 — 4 generators on 23 points:
(1,2,3)(5,7);(2,3)(4,5)(6,7);(8,10,12,18)(9,13,15,22)(11,20,21,17)(14,23,19,16);(8,9,12,15)(10,16,18,23)(11,19,21,14)(13,20,22,17)63 conjugacy classes — view the full character table.
| maximal subgroup of | #10951668, #10951669, #10951675, … |
| maximal normal subgroup of | #10951668, #10951669, #10951675, … |
| maximal quotient of | #10785370, #10785375, #10785385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16466);