Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#4511 |
| Sylow | C3 ⋊ C2×#364 |
168 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 93 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) = 96 |
A minimal faithful permutation representation — 3 generators on 21 points:
(3,4,5)(6,8,9,16,11,17,15,20,12,18,14,21,10,19,7,13);(4,5)(6,7,10,14,12,15,11,9)(8,16,17,20,18,21,19,13);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10710504, C4×#4511, #10710508, … |
| maximal normal subgroup of | #10710504, C4×#4511, #10710508, … |
| maximal quotient of | C2×#67554, #10706731, C2×#67555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3998);