Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #1789 |
618 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 105 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);(2,3)(8,10)(9,12)(11,13)(14,15);(2,3)(4,5)(6,7)(8,9,11,14,12,10,15,13)Polycyclic presentation:
2^7,3|a^2=f,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,d^b=dg,h^b=h^278 conjugacy classes — view the full character table.
| maximal subgroup of | #10686767, #10686768, #10686777, … |
| maximal normal subgroup of | #10686767, #10686768, #10686777, … |
| maximal quotient of | #10686555, #10686559, #10686564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2030);