Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | SD16×C3⋊C8 |
| Sylow | C3 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(4,5,6,8,7,9,10,11);(1,2,3)(13,16)(14,19)(17,18);(12,13,15,18)(14,16,19,17)84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C8×SD16, C2×SD16×C3⋊C8, C8×#916, … |
| maximal normal subgroup of | D3×C8×SD16, C2×SD16×C3⋊C8, C8×#916, … |
| maximal quotient of | C3⋊C8×#102, C3⋊C8×#103, C3⋊C8×#106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3469);