Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#568 ⋊ C2 |
| Sylow | C3 ⋊ #1881 |
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 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)(5,12)(6,16)(8,20)(9,24)(10,21)(11,25)(13,28)(14,29)(15,30)(17,32)(18,34)(19,23)(22,33)(26,35)(27,31);(4,6,8,22,10,18,9,17)(5,11,13,26,14,27,23,15)(7,16,20,33,21,34,24,32)(12,25,28,35,29,31,19,30);(2,3)(4,5)(6,15,18,26)(7,19)(8,13)(9,23)(10,14)(11,17,27,22)(12,20)(16,31,34,25)(21,28)(24,29)(30,32,35,33)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,d^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,d^b=dg,f^b=fg,e^c=eg66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1881, C2×#72020, #10796665, … |
| maximal normal subgroup of | D3×#1881, C2×#72020, #10796665, … |
| maximal quotient of | #10689804, #10689811, #10689818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4596);