Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1535 |
200 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 200 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) = 35 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(4,7,9,8)(5,11,12,13)(6,15,16,17)(10,18,14,19)(21,26)(25,33)(27,34)(28,35);(4,6)(5,10)(7,15)(8,17)(9,16)(11,18)(12,14)(13,19)(20,22)(21,25)(23,31)(24,30)(26,33)(27,35)(28,34)(29,32);(2,3)(4,5,8,13,9,12,7,11)(6,14,15,19,16,10,17,18)(20,21)(22,28,30,35)(23,27)(24,26)(25,29,33,31)(32,34)Polycyclic presentation:
2^7,3|a^2=e,c^2=f,d^2=g,e^2=f,b^a=bd,c^a=cg,d^a=df,h^a=h^2,d^b=dg,e^b=efg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10687527, #10687528, #10687534, … |
| maximal normal subgroup of | #10687527, #10687528, #10687534, … |
| maximal quotient of | #10683272, #10683280, #10683292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4325);