Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#382 ⋊ C2 |
| Sylow | C3 ⋊ #1958 |
336 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,3)(8,9,10,11)(13,18)(17,25)(19,23)(20,26);(2,3)(4,6,7,5)(12,14,15,21,16,22,24,27)(13,17,19,20,18,25,23,26);(4,5,7,6)(9,11)(12,13)(14,20)(15,23)(16,18)(17,21)(19,24)(22,26)(25,27)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=eg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10687730, D3×#1958, C2×#69551, … |
| maximal normal subgroup of | #10687730, D3×#1958, C2×#69551, … |
| maximal quotient of | #10693966, #10693992, #10694172, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2127);