Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×Dic3⋊C16 |
| Sylow | C3 ⋊ C2×C4⋊C16 |
184 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 25 points:
(3,4,5)(7,9)(10,11,12,15,13,16,18,21,14,17,19,22,20,23,24,25);(4,5)(6,7,8,9);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | #10682585, #10710491, C4×Dic3⋊C16, … |
| maximal normal subgroup of | #10682585, #10710491, C4×Dic3⋊C16, … |
| maximal quotient of | C2×#67554, C2×#67555, #10706785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3976);