Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1843 |
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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) = 384 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,3)(8,9,10,11)(14,20)(17,23)(21,26)(24,27);(2,3)(4,5,6,7)(12,14)(13,17)(15,21)(16,20)(18,24)(19,23)(22,26)(25,27);(5,7)(9,11)(12,13,15,18,16,19,22,25)(14,17,21,24,20,23,26,27)Polycyclic presentation:
2^7,3|a^2=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10681830, #10689302, #10689303, … |
| maximal normal subgroup of | #10681830, #10689302, #10689303, … |
| maximal quotient of | #10688938, #10688939, #10688941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3022);