Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
195 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,3,4,8)(2,5,6,7)(9,23,28)(10,17,32,16,27,31)(11,35,38)(12,13,26)(15,29,40,19,33,39)(18,25)(20,21,37)(30,34);(9,11,12,20)(10,15,16,19)(13,21,23,35)(14,22,24,36)(17,29,27,33)(18,30,25,34)(26,37,28,38)(31,39,32,40);(1,2,4,6)(3,7,8,5)(9,10,12,16)(11,19,20,15)(13,25,23,18)(14,27,24,17)(21,30,35,34)(22,29,36,33)(26,32,28,31)(37,39,38,40)Polycyclic presentation:
2^4,3,2^3|a^2=d,b^2=h,c^2=dh,f^2=h,g^2=h,b^a=bh,c^a=cd,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh40 conjugacy classes — view the full character table.
| maximal subgroup of | #11711217, #11713523, #11713524, … |
| maximal normal subgroup of | #11711217, #11713523, #11713524, … |
| maximal quotient of | #11712637, #11712694, #11712879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17915);