Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1386 |
140 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3)(8,10,13,17,14,15,20,16,12,18,21,22,19,23,11,9);(2,3)(4,5,6,7)(8,9,12,16)(10,11,18,20)(13,15,21,23)(14,22,19,17)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=fg,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^2,c^b=cg72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1386, C2×#67819, #10710104, … |
| maximal normal subgroup of | D3×#1386, C2×#67819, #10710104, … |
| maximal quotient of | #10682065, #10682114, #10682123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 395);