Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1327 |
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)(5,10,13,11)(7,15)(12,17,19,18)(14,16);(2,3)(4,5,7,12,8,11,16,18,9,13,15,19,6,10,14,17)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,d^b=deg,d^c=dg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10682573, #10682574, #10682575, … |
| maximal normal subgroup of | #10682573, #10682574, #10682575, … |
| maximal quotient of | #10681822, #10681824, #10681833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 293);