Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C23×D3×D4 (order 384) · Inn(G) = D3×D4 · Out(G) = C23 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#104 |
| Fitting | C3×#104 ⋊ C2 |
| Sylow | C3 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 11 points:
(1,3)(2,5)(4,6)(7,8)(9,10,11);(1,2,4,7,5,3,8,6);(10,11)42 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#104, #78983, D3×#421, … |
| maximal normal subgroup of | C2×D3×#104, #78983, D3×#421, … |
| maximal quotient of | D3×D4⋊C8, #68165, #68170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 379);