Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1868 |
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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)(5,11)(6,14)(8,18)(9,17)(10,20)(12,24)(13,23)(15,27)(16,28)(19,30)(21,26)(22,32)(25,34)(29,31)(33,35);(2,3)(4,6,8,16,9,15,19,29)(5,10,12,22,13,21,25,33)(7,14,18,28,17,27,30,31)(11,20,24,32,23,26,34,35);(4,5,8,12,9,13,19,25)(6,10,16,22,15,21,29,33)(7,11,18,24,17,23,30,34)(14,26,28,35,27,20,31,32)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,f^2=g,b^a=bd,c^a=ce,e^b=eg,h^b=h^2,d^c=dg60 conjugacy classes — view the full character table.
| maximal subgroup of | #10711968, #10711969, #10711975, … |
| maximal normal subgroup of | #10711968, #10711969, #10711975, … |
| maximal quotient of | #10689152, #10689157, #10689206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2578);