Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) order 12288 |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#67⋊C4 |
| Fitting | C2×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 175 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) = 96 |
A minimal faithful permutation representation — 4 generators on 13 points:
(1,2)(3,4,5)(6,7,8,9)(11,13);(1,2)(10,11)(12,13);(4,5)(11,13);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #68101, #68103, #68119, … |
| maximal normal subgroup of | #68101, #68103, #68119, … |
| maximal quotient of | C2×#4666, C2×#4649, C2×#4652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 1044);