Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#5231 |
| Fitting | C23×C3×Q8 ⋊ C2 |
| Sylow | C3 ⋊ C2×#393 |
1036 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 269 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) = 192 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,7)(8,9)(14,17,18,21)(15,19,16,20);(1,2)(10,11)(12,13)(14,16,18,15)(17,19,21,20);(1,2)(4,5)(7,9)(11,13)(14,15)(16,18)(17,19)(20,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10690173, #10690188, #10695394, … |
| maximal normal subgroup of | #10690173, #10690188, #10695394, … |
| maximal quotient of | C2×#71570, C2×#71567, C2×#72134, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16643);