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×C4⋊(C3⋊C8) |
| Sylow | C3 ⋊ C22×C4⋊C8 |
640 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 469 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)(8,9,10,11);(6,7)(9,11)(12,13,14,16,15,17,18,19);(3,4);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#67703, C2×#67654, #10684649, … |
| maximal normal subgroup of | C2×#67703, C2×#67654, #10684649, … |
| maximal quotient of | C22×#4457, C22×#4458, C2×#69729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14621);