Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
193 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 32 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) = 64 |
A minimal faithful permutation representation — 3 generators on 40 points:
(2,6)(5,8)(9,24,26)(10,17,32,16,25,31)(11,20,38,19,33,36)(12,23,14)(15,37,40)(18,22)(21,34)(28,39,30);(1,3,4,7)(2,5,6,8)(9,11)(10,15)(12,20)(13,21)(14,19)(16,30)(17,28)(18,29)(22,35)(23,36)(24,33)(25,37)(26,38)(27,34)(31,39)(32,40);(1,2)(3,5)(4,6)(7,8)(9,10,14,16)(11,15,19,30)(12,22,24,18)(13,25,27,17)(20,35,33,29)(21,37,34,28)(23,32,26,31)(36,40,38,39)Polycyclic presentation:
2^4,3,2^3|a^2=h,b^2=d,f^2=h,g^2=h,c^a=cdh,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 | C2×#85352, #11714815, #11714822, … |
| maximal normal subgroup of | C2×#85352, #11714815, #11714822, … |
| maximal quotient of | #11712666, #11712780, #11712784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17928);