Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#358 ⋊ C2 |
| Sylow | C3 ⋊ #2220 |
160 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 47 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) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(5,7)(9,15)(13,20)(16,21)(22,23);(2,3)(8,9,14,23,11,16,10,13,12,15,17,22,18,21,19,20);(2,3)(4,5)(6,7)(9,13)(10,17)(11,18)(14,19)(15,20)(16,23)(21,22)Polycyclic presentation:
2^7,3|b^2=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^2,c^b=cg,h^b=h^2,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2220, C2×#69230, #10949653, … |
| maximal normal subgroup of | D3×#2220, C2×#69230, #10949653, … |
| maximal quotient of | #10709423, #10709474, #10709542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1806);