Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1638 |
194 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(4,7,9,8)(5,11,12,16)(6,14,15,17)(10,18,19,13)(21,27)(23,24)(26,34)(28,29)(30,35)(31,32);(4,6)(5,10)(7,14)(8,17)(9,15)(11,18)(12,19)(13,16)(20,22,25,33)(21,26,29,35)(23,32,24,31)(27,34,28,30);(2,3)(4,5,9,12)(6,13,15,18)(7,11,8,16)(10,17,19,14)(20,21,25,29)(22,30,33,34)(23,28,24,27)(26,32,35,31)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=fg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^2,d^b=df,e^b=eg,d^c=dg,e^c=eg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1638, C2×#71932, #10770950, … |
| maximal normal subgroup of | D3×#1638, C2×#71932, #10770950, … |
| maximal quotient of | #10684064, #10684078, #10684120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4508);