Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C3×#358 ⋊ C2 |
| Sylow | C3 ⋊ #2242 |
138 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3)(5,9)(8,11)(12,15,16,30,32,43,34,29,19,31,33,28,18,27,17,14)(13,21,22,37,35,36,41,20,25,26,40,42,24,39,23,38);(2,3)(4,6,7,10)(5,8,9,11)(12,14,17,27,18,28,33,31,19,29,34,43,32,30,16,15)(13,20,23,36,24,37,40,21,25,38,41,39,35,42,22,26);(2,3)(4,5)(6,8)(7,9)(10,11)(12,13)(14,26)(15,20)(16,23)(17,22)(18,35)(19,25)(21,29)(24,32)(27,42)(28,39)(30,36)(31,38)(33,41)(34,40)(37,43)Polycyclic presentation:
2^7,3|b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ceg,d^a=df,e^a=efg,f^a=fg,h^a=h^2,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2242, C2×#69216, #10950485, … |
| maximal normal subgroup of | D3×#2242, C2×#69216, #10950485, … |
| maximal quotient of | #10711568, #10713101, #10713104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1792);