Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#5176 |
| Fitting | C22×C3×SD16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#496 |
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 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) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,5)(6,7)(8,9)(11,16)(12,15)(14,17);(10,11,15,16,13,17,12,14);(1,2)(4,5)(7,9)(11,14)(12,15)(16,17);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#5176, #10803728, #10803746, … |
| maximal normal subgroup of | C4×#5176, #10803728, #10803746, … |
| maximal quotient of | C2×#71258, C2×#71335, C2×#71259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16428);