Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×#101 ⋊ C2 |
| Sylow | C3 ⋊ #2049 |
254 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 65 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)(4,7,8,22,10,24,9,23)(5,12,13,29,15,30,14,20)(6,17,18,33,19,21,25,35)(11,26,16,32,27,28,31,34);(2,3)(4,6)(5,11)(7,21)(8,25)(9,18)(10,19)(12,28)(13,31)(14,16)(15,27)(17,24)(20,34)(22,33)(23,35)(26,30)(29,32);(4,5,10,15)(6,16,19,31)(7,20,24,29)(8,14,9,13)(11,25,27,18)(12,22,30,23)(17,28,21,26)(32,35,34,33)Polycyclic presentation:
2^7,3|a^2=g,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,h^b=h^2,f^c=fg,h^c=h^245 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2049, C2×#70110, #10823032, … |
| maximal normal subgroup of | D3×#2049, C2×#70110, #10823032, … |
| maximal quotient of | #10698780, #10698787, #10698794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2686);