Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1278 |
172 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 85 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 — 2 generators on 19 points:
(2,3)(4,6,8,11,9,10,7,5)(13,16,18,17);(1,2,3)(4,5,7,10,9,11,8,6)(12,13)(14,16)(15,18)(17,19)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=f,d^2=g,e^2=g,b^a=bc,c^a=cf,e^a=ef,h^b=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1278, C2×#67739, #10684681, … |
| maximal normal subgroup of | D3×#1278, C2×#67739, #10684681, … |
| maximal quotient of | #10681714, #10681726, #10681732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 315);