Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C2×D3×#15947 (order 3072) · Inn(G) = C2×D3 · Out(G) = C2×#2403 |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×(C2×D3)⋊C8 |
| Fitting | C22×C3×C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 17 points:
(3,4,5)(7,9)(10,11,12,14,13,15,16,17);(4,5)(6,7)(8,9);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #67522, #68599, #68600, … |
| maximal normal subgroup of | #67522, #68599, #68600, … |
| maximal quotient of | C2×#4459, #69734, C2×#4456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 667);