Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C16×#67 |
| Fitting | C22×C3×C16 ⋊ C2 |
| Sylow | C3 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(5,7);(2,3)(4,5)(6,7);(8,9,10,13,11,14,16,19,12,15,17,20,18,21,22,23)144 conjugacy classes — view the full character table.
| maximal subgroup of | #67⋊C32, #67×C32, #10715736, … |
| maximal normal subgroup of | #67⋊C32, #67×C32, #10715736, … |
| maximal quotient of | C16×#213, C16×#214, C16×#215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3982);