Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×#500 ⋊ C2 |
| Sylow | C3 ⋊ #1706 |
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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)(12,13,14,16,15,17,18,19);(4,5,9,11,7,10,6,8);(2,3)(5,8)(6,9)(10,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|b^2=df,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^2,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10709305, #10709306, #10709312, … |
| maximal normal subgroup of | #10709305, #10709306, #10709312, … |
| maximal quotient of | #10688955, #10694926, #10694940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3935);