Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#5126 |
| Fitting | C22×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#407 |
1008 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 285 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) = 96 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(7,9)(10,11,12,15,13,14,16,17);(1,2)(11,14)(15,17);(4,5)(6,7)(8,9);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10700417, (C2×D3)⋊#338, #10700427, … |
| maximal normal subgroup of | #10700417, (C2×D3)⋊#338, #10700427, … |
| maximal quotient of | C2×#69967, C2×#69971, C2×#70826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16336);