Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1350 |
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2)(4,6)(5,8)(7,11)(9,10)(12,14,18,28)(13,19,23,36)(15,30,33,42)(16,27,17,26)(20,37,39,40)(21,35,22,34)(24,29,41,38)(25,31,43,32);(2,3)(4,5)(6,10,11,8)(7,9)(12,13,16,21,18,23,17,22)(14,24,26,37,28,41,27,40)(15,29,31,20,33,38,32,39)(19,30,34,25,36,42,35,43)Polycyclic presentation:
2^7,3|a^2=d,b^2=g,c^2=fg,d^2=g,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^269 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1350, C2×#67529, #10705438, … |
| maximal normal subgroup of | D3×#1350, C2×#67529, #10705438, … |
| maximal quotient of | #10681876, #10681879, #10681888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 105);