Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#328 ⋊ C2 |
| Sylow | C3 ⋊ #1520 |
288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(6,11)(8,10)(12,14,16,15)(13,18,19,17);(1,2,3)(4,6,7,11)(5,8,9,10)(12,13,16,19)(14,17,15,18);(4,5)(6,10,11,8)(7,9)(13,17)(14,15)(18,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=g,d^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cf,d^b=dg,e^b=efg,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1520, C2×#68339, #10762511, … |
| maximal normal subgroup of | D3×#1520, C2×#68339, #10762511, … |
| maximal quotient of | #10683183, #10683187, #10683249, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 915);