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.
| Fitting | C2×C3×Q16 ⋊ 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)(4,7,10,20)(5,12,14,28)(6,15,9,18)(8,22,24,35)(11,26,25,27)(13,29,30,31)(16,32,23,19)(17,33,34,21);(4,6,10,9)(5,11,14,25)(7,18,20,15)(8,16,24,23)(12,27,28,26)(13,21,30,33)(17,29,34,31)(19,35,32,22);(2,3)(4,5)(6,11)(7,17)(8,21)(9,25)(10,14)(12,19)(13,23)(15,31)(16,30)(18,29)(20,34)(22,26)(24,33)(27,35)(28,32)Polycyclic presentation:
2^6,3|b^2=f,c^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 | #69264, #69272, #69273, … |
| maximal normal subgroup of | #69264, #69272, #69273, … |
| maximal quotient of | #70596, #70598, #70599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 738);