Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1915 |
308 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 89 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)(6,15)(8,22)(9,19)(10,23)(12,18)(13,29)(14,20)(16,30)(17,32)(21,31)(24,35)(25,33)(26,27)(28,34);(4,6,14,17,9,16,8,21)(5,10,13,28,12,25,27,24)(7,15,20,32,19,30,22,31)(11,23,29,34,18,33,26,35);(2,3)(4,5,8,13,9,12,14,27)(6,10,17,24,16,25,21,28)(7,18,20,29,19,11,22,26)(15,23,31,34,30,33,32,35)Polycyclic presentation:
2^7,3|a^2=f,b^2=dfg,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,d^b=dg,e^b=eg,f^b=fg,d^c=dg,f^c=fg63 conjugacy classes — view the full character table.
| maximal subgroup of | #10710972, #10710977, #10710979, … |
| maximal normal subgroup of | #10710972, #10710977, #10710979, … |
| maximal quotient of | #10690727, #10690737, #10691180, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4607);