Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1379 |
136 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 77 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 — 2 generators on 39 points:
(1,2)(4,5,6,7)(8,10)(9,15)(11,24)(12,26)(13,21)(14,23)(16,32)(17,34)(18,20)(19,31)(22,28)(25,38)(27,29)(30,36)(33,37)(35,39);(2,3)(8,9,12,17,13,18,27,35,14,19,28,36,11,16,25,33)(10,20,22,37,21,31,38,34,23,32,26,39,24,15,29,30)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,h^a=h^2,c^b=cg,d^b=dg,h^b=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1379, C2×#67815, #10710058, … |
| maximal normal subgroup of | D3×#1379, C2×#67815, #10710058, … |
| maximal quotient of | #10682027, #10682034, #10682041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 391);