Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#824 |
| Sylow | C3 ⋊ C22×#101 |
736 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 736 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) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(5,6,7)(8,10,11,17,12,18,20,23)(9,13,14,21,15,16,19,22);(6,7)(8,9,12,15)(10,16,18,13)(11,19,20,14)(17,21,23,22);(3,4);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10700508, #10700511, #10700553, … |
| maximal normal subgroup of | #10700508, #10700511, #10700553, … |
| maximal quotient of | C22×#4469, C2×#70786, C2×#69971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16349);