Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#7622880 (order 3072) · Inn(G) = #217 · Out(G) = C23×D4 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #413 |
150 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)(5,10)(6,12)(7,14)(15,19);(4,6)(5,9)(7,13)(8,12)(10,16)(11,15)(14,18)(17,19);(2,3)(4,5,7,11,8,10,14,17)(6,9,13,15,12,16,18,19)Polycyclic presentation:
2^6,3|a^2=d,d^2=f,c^a=ce,e^a=ef,g^a=g^2,c^b=cf,d^c=df42 conjugacy classes — view the full character table.
| maximal subgroup of | #67692, #67693, #67697, … |
| maximal normal subgroup of | #67692, #67693, #67697, … |
| maximal quotient of | #71571, #71572, #71587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 796);