Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#332 ⋊ C2 |
| Sylow | C3 ⋊ #1681 |
182 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(5,9)(7,11)(8,10);(2,3)(5,8)(9,10)(12,13,17,19,15,18,14,16);(2,3)(4,5)(6,8)(7,9)(10,11)(13,16)(14,17)(18,19)Polycyclic presentation:
2^7,3|b^2=dfg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^2,h^b=h^2,e^c=eg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1681, C2×#68446, #10777498, … |
| maximal normal subgroup of | D3×#1681, C2×#68446, #10777498, … |
| maximal quotient of | #10688260, #10691337, #10691369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1022);