Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1515 |
208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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 — 3 generators on 35 points:
(1,2,3)(4,7,8,15)(5,10,11,17)(6,13,14,19)(9,16,12,18)(21,26)(25,34)(27,31)(28,35);(2,3)(4,6,8,14)(5,9,11,12)(7,13,15,19)(10,16,17,18)(20,22,24,30)(21,25,26,34)(23,32,33,29)(27,35,31,28);(2,3)(4,5)(6,12,14,9)(7,10)(8,11)(13,18,19,16)(15,17)(20,21)(22,28)(23,31)(24,26)(25,29)(27,33)(30,35)(32,34)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=fg,d^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^2,d^b=dg,e^b=efg,h^b=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10687598, #10687599, #10687601, … |
| maximal normal subgroup of | #10687598, #10687599, #10687601, … |
| maximal quotient of | #10683278, #10683312, #10683314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3413);