Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C3 ⋊ #1705 |
214 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)(12,13,14,16,15,17,18,19);(2,3)(4,5,6,8,7,9,10,11);(5,8)(6,10)(9,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|b^2=d,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10683058, #10683060, #10708946, … |
| maximal normal subgroup of | #10683058, #10683060, #10708946, … |
| maximal quotient of | #10688953, #10694919, #10694920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3830);