Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#131 ⋊ C2 |
| Sylow | C3 ⋊ #3062 |
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 149 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) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(9,15)(10,16)(13,20)(17,22);(5,7)(8,10)(9,14)(11,17)(12,16)(13,19)(15,21)(18,22)(20,23);(8,9,11,13,12,15,18,20)(10,14,17,19,16,21,22,23);(2,3)(4,5)(6,7)(9,13)(11,18)(14,19)(15,20)(17,22)(21,23)Polycyclic presentation:
2^7,3|b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,d^b=dg,d^c=dg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10843154, #10843159, #10843169, … |
| maximal normal subgroup of | #10843154, #10843159, #10843169, … |
| maximal quotient of | #10778671, #10778693, #10778715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16378);