Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#6499874 (order 3072) · Inn(G) = #217 · Out(G) = C23×D4 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#834 |
| Sylow | C3 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 71 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)(6,7)(8,10)(9,11)(12,13);(4,5)(7,10,11,13)(8,12);(1,2)42 conjugacy classes — view the full character table.
| maximal subgroup of | #67637, #67641, #67695, … |
| maximal normal subgroup of | #67637, #67641, #67695, … |
| maximal quotient of | C2×#4525, #71539, C2×#4526, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 778);