Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C27×D3 (order 768) · Inn(G) = C2×D3 · Out(G) = C26 |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×#67 |
| Fitting | C22×C3×C8 ⋊ C2 |
| Sylow | C3 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 134 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) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(5,7);(2,3)(4,5)(6,7);(8,9,10,12,11,13,14,15)72 conjugacy classes — view the full character table.
| maximal subgroup of | #67⋊C16, #69102, #69103, … |
| maximal normal subgroup of | #67⋊C16, #69102, #69103, … |
| maximal quotient of | C8×(C2×D3)⋊C4, C8×Dic3⋊C4, #69784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 668);