Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1982 |
428 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 129 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)(8,9,10,11);(2,3)(4,6,7,5)(13,16)(14,19)(17,18);(2,3)(4,5,7,6)(9,11)(12,13,14,17,15,18,19,16)Polycyclic presentation:
2^7,3|a^2=f,b^2=dfg,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^2,d^b=dg,f^b=fg,h^b=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10687096, #10687097, #10687138, … |
| maximal normal subgroup of | #10687096, #10687097, #10687138, … |
| maximal quotient of | #10694144, #10694162, #10694231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4337);