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 ⋊ #3063 |
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 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) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(8,11)(9,14)(10,18)(12,21)(13,20)(15,19)(16,22)(17,23);(5,7)(11,20)(14,22)(18,19)(21,23);(8,10,12,9,13,15,17,16)(11,19,21,22,20,18,23,14);(2,3)(4,5)(6,7)(8,9,13,16)(10,17,15,12)(11,14,20,22)(18,23,19,21)Polycyclic presentation:
2^7,3|a^2=g,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 | #10843184, #10843189, #10843199, … |
| maximal normal subgroup of | #10843184, #10843189, #10843199, … |
| maximal quotient of | #10778682, #10778704, #10778726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16384);