Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1381 |
128 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 73 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:
(2,3)(4,5,6,7)(8,10,13,24,12,23,27,38,14,25,28,39,26,37,11,22)(9,15,18,30,19,31,34,36,20,32,33,35,17,29,16,21);(1,2,3)(8,9,12,17,14,20,26,19)(10,21,23,35,25,36,37,30)(11,18,13,16,27,33,28,34)(15,24,29,38,32,39,31,22)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1381, C2×#67728, #10710075, … |
| maximal normal subgroup of | D3×#1381, C2×#67728, #10710075, … |
| maximal quotient of | #10682056, #10682104, #10682106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 304);