Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×D4×#120 (order 3072) · Inn(G) = C2×#67 · Out(G) = C23×D4 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #476 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(13,16)(14,19)(17,18);(4,6,7,11)(5,8,9,10);(2,3)(4,5,7,9)(6,10,11,8)(12,13,15,18)(14,16,19,17)Polycyclic presentation:
2^6,3|a^2=ef,b^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^2,d^c=df39 conjugacy classes — view the full character table.
| maximal subgroup of | #68181, #68188, #68189, … |
| maximal normal subgroup of | #68181, #68188, #68189, … |
| maximal quotient of | #69460, #69467, #69489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 567);