Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ #3036 |
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(9,13)(12,14);(9,12)(10,15)(13,14);(2,3)(4,5,6,7);(5,7)(8,9)(10,12)(11,13)(14,15)Polycyclic presentation:
2^7,3|b^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^b=h^2,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10829755, #10829759, #10829766, … |
| maximal normal subgroup of | #10829755, #10829759, #10829766, … |
| maximal quotient of | #10778962, #10778968, #10778973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16507);