Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #73011 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
95 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,6,8,4,7,3,5)(9,19,21)(10,20,24)(11,18,13)(14,23,16);(2,5)(3,6)(7,8)(9,10,13,16)(11,17,19,15)(12,20,22,14)(18,24,21,23)Polycyclic presentation:
2^4,3,2^3|a^2=h,b^2=cd,c^2=d,f^2=h,g^2=h,b^a=bc,c^a=cd,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh37 conjugacy classes — view the full character table.
| maximal subgroup of | #11711462, #11711463, #11711466, … |
| maximal normal subgroup of | #11711462, #11711463, #11711466, … |
| maximal quotient of | #11711071, #11711181, #11711473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5589);