Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4979 |
| Sylow | C3 ⋊ C2×#395 |
908 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 277 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 — 4 generators on 21 points:
(3,4,5)(6,8,9,7)(11,13);(1,2)(6,7)(8,9)(14,16,17,21)(15,18,19,20);(4,5)(10,11)(12,13)(14,15,17,19)(16,20,21,18);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10690179, #10690181, #10690184, … |
| maximal normal subgroup of | #10690179, #10690181, #10690184, … |
| maximal quotient of | C2×#69409, C2×#71565, C2×#71568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14740);