Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#137 ⋊ C2 |
| Sylow | C3 ⋊ #3011 |
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3)(11,22)(15,29)(19,33)(23,35)(27,38)(30,36)(32,39)(34,37);(2,3)(5,7)(8,11)(9,15)(10,19)(12,23)(13,22)(14,27)(16,30)(17,29)(18,32)(20,34)(21,33)(24,36)(25,37)(26,35)(28,38)(31,39);(2,3)(8,10,13,21)(9,14,17,28)(11,19,22,33)(12,25,26,20)(15,27,29,38)(16,31,24,18)(23,37,35,34)(30,39,36,32);(4,5)(6,7)(8,9,13,17)(10,18,21,31)(11,15,22,29)(12,24,26,16)(14,25,28,20)(19,32,33,39)(23,36,35,30)(27,37,38,34)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,h^b=h^2,d^c=dg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10826712, #10826719, #10832598, … |
| maximal normal subgroup of | #10826712, #10826719, #10832598, … |
| maximal quotient of | #10768380, #10768468, #10768555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16559);