Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1802 |
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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)(13,16)(14,19)(17,18);(2,3)(8,9,10,11);(4,5,6,7)(9,11)(12,13)(14,16)(15,18)(17,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^b=h^2,e^c=eg66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1802, C2×#70153, #10794657, … |
| maximal normal subgroup of | D3×#1802, C2×#70153, #10794657, … |
| maximal quotient of | #10687868, #10687888, #10687908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2729);