Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ #3003 |
994 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(9,13)(12,14);(2,3)(5,7);(9,12)(10,15)(13,14);(4,5)(6,7)(8,9)(10,12)(11,13)(14,15)Polycyclic presentation:
2^7,3|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10826518, #10826521, #10826555, … |
| maximal normal subgroup of | #10826518, #10826521, #10826555, … |
| maximal quotient of | #10767555, #10767594, #10767633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16520);