Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#4454 |
| Sylow | C3 ⋊ C2×#322 |
248 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 173 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)(7,10)(11,13)(14,15,16,18,17,19,20,21);(4,5)(6,7,8,11,9,10,12,13);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | #10682035, #10682037, #10682161, … |
| maximal normal subgroup of | #10682035, #10682037, #10682161, … |
| maximal quotient of | C4×#4454, C2×C3⋊#1273, #10685610, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2297);