Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1839 |
240 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 240 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) = 384 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,3)(13,17)(16,19)(20,22,23,27)(21,25,24,26);(2,3)(12,14,15,18)(13,16,17,19)(21,24)(25,26);(4,5,6,8,7,9,10,11)(12,13)(14,16)(15,17)(18,19)(20,21)(22,26)(23,24)(25,27)Polycyclic presentation:
2^7,3|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^b=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | #10683206, #10683208, #10683211, … |
| maximal normal subgroup of | #10683206, #10683208, #10683211, … |
| maximal quotient of | #10688904, #10688905, #10688906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1183);