Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25 |
| direct product | D3×#336 |
| Fitting | C3×#336 ⋊ C2 |
| Sylow | C3 ⋊ C2×#336 |
528 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 213 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:
(1,2,3,4)(6,8)(17,18,19);(5,6)(7,8)(9,10,11,13,12,14,15,16);(18,19)120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1270, D3×#1271, D3×#1272, … |
| maximal normal subgroup of | D3×#1270, D3×#1271, D3×#1272, … |
| maximal quotient of | D3×#1273, #10684567, #10684571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1235);