Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#519 ⋊ C2 |
| Sylow | C3 ⋊ #1912 |
314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 314 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)(4,7,10,23)(5,12,14,20)(6,16,18,32)(8,22,9,21)(11,25,26,34)(13,28,24,27)(15,29,30,35)(17,33,19,31);(4,6)(5,11,14,26)(7,16)(8,17)(9,19)(10,18)(12,25,20,34)(13,15,24,30)(21,31)(22,33)(23,32)(27,35,28,29);(2,3)(4,5,9,13,10,14,8,24)(6,15,19,26,18,30,17,11)(7,20,22,28,23,12,21,27)(16,29,33,25,32,35,31,34)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,e^b=eg,d^c=dg,f^c=fg63 conjugacy classes — view the full character table.
| maximal subgroup of | #10711096, #10711098, #10711101, … |
| maximal normal subgroup of | #10711096, #10711098, #10711101, … |
| maximal quotient of | #10690687, #10690697, #10690707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4239);