Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) order 3072 |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×D3×D4 |
| Fitting | C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 169 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) = 48 |
A minimal faithful permutation representation — 4 generators on 11 points:
(6,8)(9,10,11);(5,6)(7,8);(10,11);(1,2,3,4)60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4⋊C8, #68167, #68172, … |
| maximal normal subgroup of | D3×D4⋊C8, #68167, #68172, … |
| maximal quotient of | C4×#67⋊C4, C4×#878, C4×#885, … |
| automorphism group of | C5×Dic6, C5×D12, C2×C5×Dic3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 1103);