Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#61451 (order 1536) · Inn(G) = C2×#213 · Out(G) = C24 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #510 |
82 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(5,11)(6,15)(7,18)(8,19)(10,22)(12,13)(14,28)(16,32)(20,29)(21,27)(23,34)(24,35)(25,26)(30,33);(4,6)(5,10)(7,16)(8,17)(9,15)(11,26)(12,23)(13,24)(14,25)(18,33)(19,31)(20,30)(21,34)(22,28)(27,35)(29,32);(2,3)(4,5,9,14)(6,10,15,25)(7,11,20,28)(8,21,19,13)(12,29,27,18)(16,26,30,22)(17,34,31,24)(23,32,35,33)Polycyclic presentation:
2^6,3|a^2=f,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,g^a=g^2,c^b=cf,d^c=de,e^c=ef30 conjugacy classes — view the full character table.
| maximal subgroup of | #69244, #69245, #69248, … |
| maximal normal subgroup of | #69244, #69245, #69248, … |
| maximal quotient of | #70649, #70654, #70655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 754);