Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of #204 |
| automorphism | Aut(G) = C2×D3×#3484 (order 1536) · Inn(G) = D12 · Out(G) = C23×D4 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#805 |
| Fitting | C2×C3×C42 ⋊ C2 |
| Sylow | C3 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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 — 3 generators on 13 points:
(3,4,5)(7,10,11,12);(4,5)(6,7)(8,10)(9,11)(12,13);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #68646, #68694, #68695, … |
| maximal normal subgroup of | #68646, #68694, #68695, … |
| maximal quotient of | C4×#805, #69395, #69396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 486);