Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#360 |
| Fitting | C3×#360 ⋊ C2 |
| Sylow | C3 ⋊ C2×#360 |
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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(3,10)(4,13)(5,7)(6,14)(8,12)(9,15)(11,16)(17,18,19);(2,6,7,15)(3,9)(4,12)(8,10,13,16)(11,14);(18,19)48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#360, D3×#2145, #10948131, … |
| maximal normal subgroup of | C2×D3×#360, D3×#2145, #10948131, … |
| maximal quotient of | D3×#1333, D3×#1334, #10704955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1826);