Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #73085 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,3,5,11)(2,6,8,15)(4,13,14,10)(7,16,12,9)(17,27,29)(18,28,32)(19,26,21)(22,31,24);(1,2,5,8)(3,9,11,16)(4,12,14,7)(6,13,15,10)(17,18,21,24)(19,25,27,23)(20,28,30,22)(26,32,29,31)Polycyclic presentation:
2^4,3,2^3|a^2=dh,b^2=d,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,c^b=cd,f^e=g,g^e=fgh,g^f=gh31 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73098, #11711972, #11711982, … |
| maximal normal subgroup of | C2×#73098, #11711972, #11711982, … |
| maximal quotient of | #11711056, #11711094, #11711118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5674);