Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2211 |
158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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:
(2,3)(8,10,11,19)(9,15,14,29)(12,25,22,39)(13,28,23,21)(16,32,30,38)(17,33,27,31)(18,35,34,24)(20,37,36,26);(1,2,3)(4,5,6,7)(9,14)(15,29)(16,30)(17,27)(18,34)(24,35)(31,33)(32,38);(5,7)(8,9)(10,18)(11,14)(12,24)(13,27)(15,20)(16,26)(17,23)(19,34)(21,38)(22,35)(25,33)(28,32)(29,36)(30,37)(31,39)Polycyclic presentation:
2^7,3|b^2=dg,c^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,e^c=ef,f^c=fg,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2211, C2×#71324, #10949448, … |
| maximal normal subgroup of | D3×#2211, C2×#71324, #10949448, … |
| maximal quotient of | #10709321, #10709349, #10709383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3900);