Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×#442 (order 768) · Inn(G) = D3×D8 · Out(G) = C2×C4 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×Q32 ⋊ C2 |
| 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)(4,6,9,14)(5,10,13,25)(7,19,22,35)(8,24,20,17)(11,29,30,34)(12,31,23,27)(15,33,32,18)(16,28,26,21);(4,5,9,13)(6,15,14,32)(7,18,22,33)(8,23,20,12)(10,26,25,16)(11,28,30,21)(17,34,24,29)(19,31,35,27);(2,3)(6,14)(10,25)(15,32)(16,26)(17,24)(19,35)(27,31)(29,34)Polycyclic presentation:
2^6,3|b^2=f,c^2=f,d^2=ef,e^2=f,c^a=cf,g^a=g^2,c^b=cd,d^b=de,e^b=ef,d^c=de,e^c=ef27 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#4918, #82028, #82030, … |
| maximal normal subgroup of | C2×#4918, #82028, #82030, … |
| maximal quotient of | #69208, #69209, #69210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 477);