Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×#1020⋊C2 (order 2304) · Inn(G) = #953 · Out(G) = C22×D3 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #458 |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,7)(5,10)(6,12)(8,14)(9,15)(11,17)(13,19)(16,18);(4,6)(5,9)(7,12)(8,13)(10,15)(11,16)(14,19)(17,18);(2,3)(4,5,8,11)(6,9,13,16)(7,10,14,17)(12,18,19,15)Polycyclic presentation:
2^6,3|a^2=f,b^a=be,c^a=cd,g^a=g^2,d^b=df,e^c=ef33 conjugacy classes — view the full character table.
| maximal subgroup of | #70985, #70986, #70990, … |
| maximal normal subgroup of | #70985, #70986, #70990, … |
| maximal quotient of | #71655, #71657, #71843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 802);