Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1331 |
110 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 49 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 — 2 generators on 27 points:
(1,2,3)(13,17)(14,21)(15,22)(18,19)(20,26)(23,27)(24,25);(2,3)(4,5,6,8,7,9,10,11)(12,13)(14,17)(15,24)(16,20)(18,21)(19,22)(23,26)(25,27)Polycyclic presentation:
2^7,3|a^2=d,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,c^b=ce,e^b=eg72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1331, C2×#67763, #10704924, … |
| maximal normal subgroup of | D3×#1331, C2×#67763, #10704924, … |
| maximal quotient of | #10681836, #10681848, #10681954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 339);