Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1617 |
202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 202 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 — 3 generators on 35 points:
(1,2,3)(4,7,8,14)(5,10,11,17)(6,12,13,19)(9,15,16,18);(2,3)(4,6)(5,9)(7,12)(8,13)(10,15)(11,16)(14,19)(17,18)(20,22,24,30)(21,25,27,34)(23,32,33,29)(26,35,31,28);(2,3)(4,5,8,11)(6,9,13,16)(7,10,14,17)(12,18,19,15)(20,21,24,27)(22,28,30,35)(23,31,33,26)(25,32,34,29)Polycyclic presentation:
2^7,3|a^2=fg,b^2=f,c^2=g,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^2,d^b=df,e^b=eg,h^b=h^2,d^c=dg45 conjugacy classes — view the full character table.
| maximal subgroup of | #10708012, #10708013, #10708018, … |
| maximal normal subgroup of | #10708012, #10708013, #10708018, … |
| maximal quotient of | #10684254, #10684268, #10684348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 717);