Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #2230 |
126 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 49 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6)(5,11)(7,17)(8,18)(9,15)(10,16)(12,19)(13,14);(4,5,10,7,9,13,8,12)(6,11,16,17,15,14,18,19);(2,3)(5,7)(6,14,15,11)(8,10)(12,13)(16,17,18,19)Polycyclic presentation:
2^7,3|a^2=d,b^2=dfg,e^2=f,f^2=g,b^a=bdfg,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,d^c=dg,e^c=efg,f^c=fg51 conjugacy classes — view the full character table.
| maximal subgroup of | #10708946, #10708948, #10708951, … |
| maximal normal subgroup of | #10708946, #10708948, #10708951, … |
| maximal quotient of | #10711288, #10711884, #10712886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3495);