Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #504 ⋊ D3 |
85 conjugacy classes of subgroups.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 2 generators on 64 points:
(1,37,60,30,43,62,3,38,22,13,31,64,15,33,45,29,23,39,9,53,50,10,46,56,7,11,59,26,19,61,18,27,24,2,41,63,4,51,47,8,5,36,14,57,49,25,16,55)(6,12,32,58,20,34,17,28,21,40,42,54,44,52,48,35);(2,8)(3,14)(4,15)(5,21)(6,23)(9,18)(10,30)(11,35)(12,38)(13,29)(16,32)(17,31)(19,20)(22,24)(25,26)(27,40)(28,37)(33,54)(34,53)(36,56)(39,55)(41,48)(42,46)(43,44)(45,59)(47,60)(51,58)(52,57)(61,63)(62,64)Polycyclic presentation:
2^4,3,2^3|b^2=cdh,c^2=dh,d^2=h,f^2=h,g^2=h,b^a=bc,c^a=cd,d^a=dh,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73041, #11714197, #11714198, … |
| maximal normal subgroup of | C2×#73041, #11714197, #11714198, … |
| maximal quotient of | #11711472, #11711475, #11711476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5617);