Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #520 ⋊ D3 |
258 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 36 points:
(1,2,3,4)(5,18,23)(6,13,28,12,22,27)(7,16,34,15,29,32)(8,9,21)(11,33,36)(14,20)(17,30)(24,25,35);(5,7,8,15)(6,11,12,24)(9,16,18,29)(10,17,19,30)(13,25,22,33)(14,26,20,31)(21,32,23,34)(27,35,28,36);(2,4)(5,6)(7,11)(8,12)(9,20)(10,22)(13,19)(14,18)(15,24)(16,31)(17,33)(21,28)(23,27)(25,30)(26,29)(32,36)(34,35)Polycyclic presentation:
2^4,3,2^3|b^2=h,c^2=dh,f^2=h,g^2=h,c^a=cd,e^a=e^2,f^a=gh,g^a=fh,c^b=ch,f^e=g,g^e=fgh,g^f=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | #11713402, #11713404, #11713410, … |
| maximal normal subgroup of | #11713402, #11713404, #11713410, … |
| maximal quotient of | #11712238, #11712239, #11712240, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17946);