Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4537 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1526 |
226 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)(4,6,8,7)(5,9,10,11)(12,15,17,16)(13,18,14,19);(4,5)(6,9)(7,11)(8,10)(12,14,17,13)(15,19,16,18);(2,3)(5,9,10,11)(12,13,16,19,17,14,15,18)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=g,d^2=g,e^2=f,b^a=bd,d^a=df,h^a=h^2,d^b=dg,e^b=efg66 conjugacy classes — view the full character table.
| maximal subgroup of | #10686195, #10686198, #10686205, … |
| maximal normal subgroup of | #10686195, #10686198, #10686205, … |
| maximal quotient of | #10683142, #10683165, #10683434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4397);