Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #2251 |
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2)(4,5,6,7)(10,20)(14,28)(18,32)(21,27)(22,36)(29,33)(34,37)(35,39);(8,10,19,35,12,22,25,27,13,20,30,39,24,36,11,21)(9,14,23,34,16,29,31,32,17,28,38,37,26,33,15,18);(2,3)(5,7)(8,9,13,17)(10,18,20,32)(11,23,25,38)(12,26,24,16)(14,27,28,21)(15,30,31,19)(22,37,36,34)(29,35,33,39)Polycyclic presentation:
2^7,3|a^2=g,b^2=df,c^2=e,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^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2251, C2×#71482, #10950607, … |
| maximal normal subgroup of | D3×#2251, C2×#71482, #10950607, … |
| maximal quotient of | #10709861, #10709863, #10709864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4058);