Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#536 ⋊ C2 |
| Sylow | C3 ⋊ #3046 |
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(8,10,12,17)(9,14,16,21)(11,18,19,23)(13,20,15,22);(2,3)(9,13)(11,19)(14,20)(15,16)(18,23)(21,22);(4,5,6,7)(10,17)(14,21)(18,23)(20,22);(5,7)(8,9,12,16)(10,14,17,21)(11,13,19,15)(18,20,23,22)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10833251, #10833254, #10833266, … |
| maximal normal subgroup of | #10833251, #10833254, #10833266, … |
| maximal quotient of | #10780649, #10780660, #10780671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15982);