Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68807 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2066 |
248 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 248 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) = 384 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(5,7)(9,11)(12,14,16,17)(13,18,19,15);(8,9)(10,11)(12,13,18,17,16,19,15,14);(2,3)(4,5,6,7)(13,17)(14,19)(15,18)Polycyclic presentation:
2^7,3|a^2=d,b^2=deg,c^2=g,e^2=g,f^2=g,b^a=bdeg,c^a=ce,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,e^c=eg,f^c=fg60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2066, C2×#70247, #10823799, … |
| maximal normal subgroup of | D3×#2066, C2×#70247, #10823799, … |
| maximal quotient of | #10699709, #10699716, #10699765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2823);