Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#4535 |
| Sylow | C3 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 141 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 — 3 generators on 21 points:
(3,4,5)(6,7,9,11)(8,13,12,10);(4,5)(7,10)(8,12)(11,13)(14,15,16,18,17,19,20,21);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4535, Dic3×Q8⋊C8, #10685794, … |
| maximal normal subgroup of | C4×#4535, Dic3×Q8⋊C8, #10685794, … |
| maximal quotient of | C2×#67638, C2×#67642, #10683134, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4196);