Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×Dic3⋊C8 |
| Sylow | C3 ⋊ C22×C4⋊C8 |
640 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 389 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 19 points:
(5,6,7)(9,11)(12,13,14,16,15,17,18,19);(6,7)(8,9,10,11);(3,4);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | #10700972, #10700975, #10700978, … |
| maximal normal subgroup of | #10700972, #10700975, #10700978, … |
| maximal quotient of | C22×#4480, C22×#4479, C2×#70745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16303);