Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C25×D3×D4 (order 1536) · Inn(G) = D3×D4 · Out(G) = C25 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #501 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6,7,11)(5,8,9,10)(13,17)(14,19)(16,18);(12,13,14,18,15,16,19,17);(2,3)(4,5,7,9)(6,10,11,8)(13,16)(17,18)Polycyclic presentation:
2^6,3|a^2=d,b^2=e,c^2=d,e^2=f,b^a=bf,c^a=cd,g^a=g^2,c^b=ce,e^c=ef30 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#4876, #79139, #79158, … |
| maximal normal subgroup of | C2×#4876, #79139, #79158, … |
| maximal quotient of | #68805, #68806, #68827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 435);