Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#6628842 (order 3072) · Inn(G) = D3×D4 · Out(G) = C2×#120 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#106 ⋊ C2 |
| Sylow | C3 ⋊ #470 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(4,5,6,7)(9,14)(10,17)(12,19)(13,20)(16,21)(18,23);(8,10,12,17,11,18,19,23)(9,13,15,21,14,16,22,20);(2,3)(5,7)(8,9)(10,16)(11,14)(12,15)(13,18)(17,20)(19,22)(21,23)Polycyclic presentation:
2^6,3|b^2=e,c^2=df,e^2=f,b^a=bf,c^a=cd,g^a=g^2,c^b=cef,e^c=ef30 conjugacy classes — view the full character table.
| maximal subgroup of | #69253, #69314, C2×#4867, … |
| maximal normal subgroup of | #69253, #69314, C2×#4867, … |
| maximal quotient of | #68541, #68543, #68545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 426);