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) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #442 |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(9,12)(10,14)(13,15);(8,10)(9,13)(11,15)(12,14);(2,3)(4,5,6,7)(8,9,11,12)(10,13,15,14)Polycyclic presentation:
2^6,3|a^2=d,e^2=f,c^a=cf,g^a=g^2,c^b=ce,e^b=ef,e^c=ef36 conjugacy classes — view the full character table.
| maximal subgroup of | #69254, #71515, #79576, … |
| maximal normal subgroup of | #69254, #71515, #79576, … |
| maximal quotient of | #70152, #70156, #70170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 711);