Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1736 |
448 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)(13,18)(17,19);(2,3)(8,9,10,11)(12,13,15,19,16,18,14,17);(2,3)(4,5,6,7)(13,17)(14,15)(18,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^2,c^b=cg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10700516, #10700517, #10700550, … |
| maximal normal subgroup of | #10700516, #10700517, #10700550, … |
| maximal quotient of | #10684650, #10684660, #10684672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4157);