Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) order 6144 |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#908 |
| Fitting | C2×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 13 points:
(3,4,5)(6,7,8,10,9,11,12,13);(1,2)(7,11)(10,13);(4,5)(7,10)(8,12)(11,13);(1,2)42 conjugacy classes — view the full character table.
| maximal subgroup of | #68704, #68726, #68761, … |
| maximal normal subgroup of | #68704, #68726, #68761, … |
| maximal quotient of | C2×#4702, C2×#4710, C2×#4711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 1305);