Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C22×D3×#3003 (order 3072) · Inn(G) = D3×D4 · Out(G) = C23×D4 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×#107 ⋊ C2 |
| Sylow | C3 ⋊ #427 |
114 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)(10,16)(11,19)(13,20)(17,18)(21,23);(8,10,11,17,12,18,19,16)(9,13,15,20,14,21,22,23);(2,3)(8,9)(10,13)(11,15)(12,14)(16,23)(17,20)(18,21)(19,22)Polycyclic presentation:
2^6,3|b^2=e,c^2=d,e^2=f,c^a=cf,g^a=g^2,c^b=ce,e^c=ef42 conjugacy classes — view the full character table.
| maximal subgroup of | #69182, #69188, #69190, … |
| maximal normal subgroup of | #69182, #69188, #69190, … |
| maximal quotient of | #68567, #68570, #68573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 439);