Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#4463 |
| Sylow | C3 ⋊ C2×#364 |
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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)(6,8,10,18,12,19,11,9)(7,13,15,17,16,14,20,21);(4,5)(6,7,9,14,11,15,19,21,12,16,18,13,10,20,8,17);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10682070, #10682071, #10682072, … |
| maximal normal subgroup of | #10682070, #10682071, #10682072, … |
| maximal quotient of | C2×#67439, #10706732, C2×#67440, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2322);