Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C3×#106 ⋊ C2 |
| Sylow | C3 ⋊ #1972 |
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 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) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(12,14,16,13,17,18,15,19);(2,3)(4,6,7,5)(9,11)(12,13,16,18,17,19,15,14);(4,5,7,6)(8,9,10,11)(13,14)(15,16)(18,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=dfg,c^2=e,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10712333, #10712336, #10712438, … |
| maximal normal subgroup of | #10712333, #10712336, #10712438, … |
| maximal quotient of | #10694058, #10694092, #10694356, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3152);