Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#525 (order 384) · Inn(G) = (C2×D3)⋊C4 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ #349 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(4,5,6,10,7,11,13,17,8,9,12,15,14,16,18,19);(2,3)(5,9)(6,12)(11,16)(13,18)Polycyclic presentation:
2^6,3|b^2=c,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^2,d^b=df42 conjugacy classes — view the full character table.
| maximal subgroup of | #69088, #69089, D3×#349, … |
| maximal normal subgroup of | #69088, #69089, D3×#349, … |
| maximal quotient of | #67515, #67518, #67522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 73);