Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #69507 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2042 |
318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 87 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:
(2,3)(5,7)(8,10,11,9)(13,18)(14,19)(15,16);(1,2,3)(8,9)(10,11)(12,14)(13,15)(16,19)(17,18);(4,5)(6,7)(9,10)(12,13,17,19)(14,15,18,16)Polycyclic presentation:
2^7,3|a^2=g,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,e^b=eg,f^b=fg,e^c=eg,f^c=fg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2042, C2×#71722, #10822872, … |
| maximal normal subgroup of | D3×#2042, C2×#71722, #10822872, … |
| maximal quotient of | #10698518, #10698525, #10698556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4298);