Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1392 |
158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 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 — 2 generators on 35 points:
(1,2,3)(4,6,8,16,9,17,20,30)(5,10,13,23,11,14,25,28)(7,15,19,29,18,21,31,32)(12,26,27,35,24,22,33,34);(2,3)(4,5,7,12,9,11,18,24)(6,14,15,26,17,10,21,22)(8,13,19,27,20,25,31,33)(16,28,29,35,30,23,32,34)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=g,e^2=g,b^a=bc,c^a=cf,f^a=fg,h^a=h^2,d^b=df,d^c=dg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10682688, #10682689, #10682691, … |
| maximal normal subgroup of | #10682688, #10682689, #10682691, … |
| maximal quotient of | #10682148, #10682182, #10682221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 269);