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.
112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,7,8)(2,6,4)(9,11,13,19)(10,14,16,23)(12,21,22,18)(15,24,20,17);(2,5)(3,7)(6,8)(9,10,13,16)(11,17,19,24)(12,20,22,15)(14,21,23,18)Polycyclic presentation:
2^4,3,2^3|a^2=d,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×#73099, #11711977, #11711981, … |
| maximal normal subgroup of | C2×#73099, #11711977, #11711981, … |
| maximal quotient of | #11711056, #11711096, #11711120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5675);