Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2223 |
144 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 47 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:
(1,2,3)(4,6)(5,13)(7,18)(8,22)(9,17)(10,19)(11,23)(12,27)(14,31)(15,29)(16,30)(20,32)(21,33)(24,35)(25,28)(26,34);(2,3)(4,5,12,24,9,15,7,11,10,16,20,25,8,14,21,26)(6,13,27,35,17,29,18,23,19,30,32,28,22,31,33,34);(5,11)(6,17)(7,20)(8,9)(12,21)(13,28)(14,25)(15,24)(16,26)(18,33)(19,22)(23,29)(30,35)(31,34)Polycyclic presentation:
2^7,3|b^2=dfg,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^b=h^2,e^c=eg42 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2223, C2×#71093, #10949760, … |
| maximal normal subgroup of | D3×#2223, C2×#71093, #10949760, … |
| maximal quotient of | #10709401, #10709418, #10709452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3669);