Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D3×#330 |
| Fitting | C3×#330 ⋊ C2 |
| Sylow | C3 ⋊ C2×#330 |
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 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) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(3,7)(4,6)(5,8)(9,11,14,10)(12,15,13,16)(17,18,19);(2,5,6,7)(9,10,13,15,14,11,12,16);(18,19)57 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#330, D3×#1524, D3×#1526, … |
| maximal normal subgroup of | C2×D3×#330, D3×#1524, D3×#1526, … |
| maximal quotient of | D3×#1271, #10683157, #10683411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 936);