Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C3⋊#1308 |
| Sylow | C3 ⋊ #1308 |
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 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) = 192 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3)(4,6)(5,9,11,12)(7,14)(8,13)(10,17,18,19)(15,16)(20,22,24,29,23,28,30,34)(21,25,27,32,26,33,31,35);(2,3)(4,5,7,10,8,11,15,18)(6,12,14,19,13,9,16,17)(20,21,23,26)(22,25)(24,31,30,27)(28,33)(29,35)(32,34)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=fg,e^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^2,c^b=cg,d^b=df54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1308, C2×C3⋊#1308, #10685589, … |
| maximal normal subgroup of | D3×#1308, C2×C3⋊#1308, #10685589, … |
| maximal quotient of | #10681759, #10681760, #10681761, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 335);