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.
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,4,6)(3,8,7,5)(9,15,19,10,20,23,14,17,21,11,12,24)(13,18,22,16);(2,5)(3,7)(6,8)(9,10,14,11)(12,18,20,16)(13,17,22,15)(19,24,21,23)Polycyclic presentation:
2^4,3,2^3|a^2=h,b^2=dh,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×#73094, #11711967, #11711980, … |
| maximal normal subgroup of | C2×#73094, #11711967, #11711980, … |
| maximal quotient of | #11711055, #11711095, #11711121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5670);