Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D3×#441 |
| Fitting | C3×#441 ⋊ C2 |
| Sylow | C3 ⋊ C2×#441 |
480 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,3,4,2)(6,11)(10,19)(12,16)(13,20)(21,22,23);(5,7,9,15)(6,10,11,19)(8,17,18,14)(12,20,16,13);(1,2,4,3)(5,6)(7,13)(8,16)(9,11)(10,14)(12,18)(15,20)(17,19);(22,23)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2180, C2×D3×#441, D3×#2943, … |
| maximal normal subgroup of | D3×#2180, C2×D3×#441, D3×#2943, … |
| maximal quotient of | D3×#1579, D3×#1587, D3×#1593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12403);