Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
202 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 40 points:
(2,6)(3,7)(9,36,24,22,25,37,14,20,27,11,12,35)(10,33,31,19,26,40,18,29,32,15,16,39)(13,21,28,38)(17,30,23,34);(1,3,4,7)(2,5,6,8);(1,2)(3,5)(4,6)(7,8)(9,10,14,18)(11,19,22,15)(12,23,25,17)(13,26,28,16)(20,30,36,34)(21,29,38,33)(24,32,27,31)(35,39,37,40)Polycyclic presentation:
2^4,3,2^3|a^2=h,b^2=d,c^2=h,f^2=h,g^2=h,c^a=cdh,e^a=e^2,f^a=gh,g^a=fh,c^b=cd,f^e=g,g^e=fgh,g^f=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | #11712286, #11712290, #11712333, … |
| maximal normal subgroup of | #11712286, #11712290, #11712333, … |
| maximal quotient of | #11712916, #11712993, #11713039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17982);