Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4466 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1375 |
140 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 77 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:
(2,3)(5,7)(9,14,17,15)(11,19)(16,22,23,21)(18,20);(1,2,3)(4,5)(6,7)(8,9,11,16,12,14,20,21,13,17,19,23,10,15,18,22)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,e^a=eg,d^b=dg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1375, C2×#67811, #10710035, … |
| maximal normal subgroup of | D3×#1375, C2×#67811, #10710035, … |
| maximal quotient of | #10682016, #10682028, #10682035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 387);