Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#494 ⋊ C2 |
| Sylow | C3 ⋊ D4×Q16 |
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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)(8,11,13,22)(9,15,16,12)(10,18,20,14)(17,23,21,19);(2,3)(5,7);(2,3)(8,10,13,20)(9,14,16,18)(11,21,22,17)(12,23,15,19);(4,5)(6,7)(8,9,13,16)(10,17,20,21)(11,12,22,15)(14,23,18,19)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^b=h^2,h^c=h^2,e^d=eg,h^d=h^257 conjugacy classes — view the full character table.
| maximal subgroup of | #10708622, #10708626, #10708650, … |
| maximal normal subgroup of | #10708622, #10708626, #10708650, … |
| maximal quotient of | #10785373, #10785388, #10785403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14383);