Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68629 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2001 |
392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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)(5,7)(9,11);(2,3)(8,9)(10,11)(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20);(2,3)(4,5)(6,7)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,c^b=cf,d^b=dg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10681865, #10681867, #10681889, … |
| maximal normal subgroup of | #10681865, #10681867, #10681889, … |
| maximal quotient of | #10695455, #10695462, #10695483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2540);