Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#61451 (order 1536) · Inn(G) = #809 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #362 |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3)(4,6,7,15,9,18,21,17)(5,10,11,26,13,28,19,27)(8,23,20,25,24,34,29,16)(12,30,22,33,31,32,35,14);(2,3)(4,5,9,13)(6,14,18,33)(7,19,21,11)(8,22,24,35)(10,25,28,16)(12,29,31,20)(15,32,17,30)(23,27,34,26)Polycyclic presentation:
2^6,3|a^2=f,b^2=c,c^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^2,d^b=def,e^b=ef30 conjugacy classes — view the full character table.
| maximal subgroup of | #69243, #69245, #69256, … |
| maximal normal subgroup of | #69243, #69245, #69256, … |
| maximal quotient of | #67466, #67474, #67475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 55);