Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1657 |
206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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:
(2,3)(4,5)(6,11)(7,9)(8,10)(12,14,16,21)(13,18,19,27)(15,24,22,20)(17,25,23,26);(1,2,3)(6,10)(8,11)(12,13)(14,18)(15,23)(16,19)(17,22)(20,25)(21,27)(24,26);(5,8)(6,10)(9,11)(13,17)(15,22)(18,26)(19,23)(20,24)(25,27)Polycyclic presentation:
2^7,3|c^2=f,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,d^b=df,e^b=eg,d^c=dg,e^c=efg,h^c=h^236 conjugacy classes — view the full character table.
| maximal subgroup of | #10715933, #10715936, D3×#1657, … |
| maximal normal subgroup of | #10715933, #10715936, D3×#1657, … |
| maximal quotient of | #10683894, #10683907, #10683920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3904);