Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1953 |
184 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 79 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) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2)(4,7,8,21,10,23,9,22)(5,12,13,20,14,28,24,34)(6,16,18,31,19,32,17,30)(11,25,26,33,27,35,15,29);(2,3)(4,6,9,17,10,19,8,18)(5,11,13,26,14,27,24,15)(7,16,22,30,23,32,21,31)(12,25,20,33,28,35,34,29);(4,5,9,13,10,14,8,24)(6,15,17,11,19,26,18,27)(7,20,22,28,23,34,21,12)(16,25,30,33,32,35,31,29)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,h^b=h^2,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1953, C2×#69015, #10798757, … |
| maximal normal subgroup of | D3×#1953, C2×#69015, #10798757, … |
| maximal quotient of | #10693797, #10693802, #10693807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1591);