Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2216 |
154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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:
(1,2,3)(5,7);(2,3)(8,10,19,35,12,21,25,27,13,22,30,39,24,36,11,20)(9,14,23,33,16,28,31,34,17,29,38,37,26,32,15,18);(4,5)(6,7)(8,9,13,17)(10,18,22,34)(11,23,25,38)(12,26,24,16)(14,27,29,20)(15,30,31,19)(21,37,36,33)(28,35,32,39)Polycyclic presentation:
2^7,3|a^2=g,b^2=df,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2216, C2×#71081, #10949623, … |
| maximal normal subgroup of | D3×#2216, C2×#71081, #10949623, … |
| maximal quotient of | #10709396, #10709447, #10709515, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3657);