Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×#405 ⋊ C2 |
| Sylow | C3 ⋊ #3156 |
532 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 165 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 — 4 generators on 39 points:
(1,2,3)(11,23)(15,29)(20,34)(24,33)(27,38)(30,36)(31,39)(35,37);(4,5,6,7)(8,11)(9,15)(10,20)(12,24)(13,23)(14,27)(16,30)(17,29)(18,31)(19,33)(21,35)(22,34)(25,36)(26,37)(28,38)(32,39);(8,10,19,26,13,22,12,21)(9,14,25,32,17,28,16,18)(11,20,33,37,23,34,24,35)(15,27,36,39,29,38,30,31);(2,3)(5,7)(8,9,13,17)(10,18,22,32)(11,15,23,29)(12,25,19,16)(14,26,28,21)(20,31,34,39)(24,36,33,30)(27,37,38,35)Polycyclic presentation:
2^7,3|a^2=g,b^2=eg,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,d^c=dg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10713462, #10713464, #10714076, … |
| maximal normal subgroup of | #10713462, #10713464, #10714076, … |
| maximal quotient of | #10783063, #10783107, #10783125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11152);