Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ #2006 |
406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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 — 3 generators on 15 points:
(1,2,3)(5,7)(8,9)(10,13)(11,15)(12,14);(2,3)(4,5)(6,7)(8,9)(10,15)(11,13)(12,14);(9,13)(10,11)(14,15)Polycyclic presentation:
2^7,3|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,h^b=h^2,e^c=eg48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2006, C2×#72098, #10822150, … |
| maximal normal subgroup of | D3×#2006, C2×#72098, #10822150, … |
| maximal quotient of | #10695492, #10695493, #10695499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4674);