Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4851 |
| Sylow | C3 ⋊ C2×#475 |
416 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 173 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)(7,11)(8,12)(14,16,17,19,18,20,21,15);(1,2)(6,8,9,12)(7,10,11,13);(4,5)(6,7)(8,10)(9,11)(12,13)(14,15,18,19)(16,17,20,21);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10689982, #10689984, #10689989, … |
| maximal normal subgroup of | #10689982, #10689984, #10689989, … |
| maximal quotient of | C2×#70485, C2×#68684, C2×#68622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11610);