Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #73011 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,5,4,6,7,8)(9,17,22)(10,15,24,14,21,23)(11,12,20)(16,19);(2,5)(3,7)(6,8)(9,10,11,14)(12,19,17,16)(13,21,18,15)(20,24,22,23)Polycyclic presentation:
2^4,3,2^3|a^2=h,b^2=ch,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 | C2×#73011, #11712170, #11712171, … |
| maximal normal subgroup of | C2×#73011, #11712170, #11712171, … |
| maximal quotient of | #11711072, #11711181, #11711182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5587);