Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1336 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(4,6)(5,9)(7,11)(8,12)(10,17)(13,18)(14,16)(15,19);(2,3)(4,5,7,11,8,13,17,10,9,6,14,16,18,12,19,15)Polycyclic presentation:
2^7,3|a^2=d,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,c^b=ceg,d^b=dg,e^b=eg60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1336, C2×#67767, #10704980, … |
| maximal normal subgroup of | D3×#1336, C2×#67767, #10704980, … |
| maximal quotient of | #10681842, #10681845, #10681848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 343);