Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4537 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4547 |
| Sylow | C3 ⋊ C2×#332 |
256 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 21 points:
(3,4,5)(6,7)(8,13)(9,11)(10,12)(14,16,19,15)(17,20,18,21);(4,5)(7,10)(8,12)(11,13)(14,15,17,20,19,16,18,21);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4547, Dic3×#332, #10686148, … |
| maximal normal subgroup of | C4×#4547, Dic3×#332, #10686148, … |
| maximal quotient of | C2×#67638, #10683165, #10683467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4347);