Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ #1898 |
598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 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 — 3 generators on 15 points:
(2,3)(5,7);(1,2,3)(8,10)(9,12,13,15)(11,14);(4,5)(6,7)(8,9)(10,12,14,15)(11,13)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,b^a=bd,c^a=ce,d^a=dg,d^b=dg,f^b=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1898, C2×#70036, #10796977, … |
| maximal normal subgroup of | D3×#1898, C2×#70036, #10796977, … |
| maximal quotient of | #10690555, #10690565, #10690575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2612);