Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 2 generators on 64 points:
(1,47,52,16,6,46,4,43,29,3,20,63,8,17,54,15,27,49,5,41,26,19,23,64)(2,56,60,14,11,57,22,38,37,9,53,62,13,31,59,40,28,58,10,48,36,33,34,61)(7,18,24,44,30,50,21,42)(12,32,35,39,25,55,51,45);(1,2,4,10,8,13,5,22)(3,14,15,33,19,40,16,9)(6,25,20,51,27,12,23,35)(7,28,21,53,30,11,24,34)(17,45,41,32,47,39,43,55)(18,48,42,31,50,38,44,56)(26,37,52,60,29,36,54,59)(46,62,63,57,49,61,64,58)Polycyclic presentation:
2^4,3,2^3|a^2=c,b^2=d,c^2=h,d^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh40 conjugacy classes — view the full character table.
| maximal subgroup of | #11711520, #11711523, #11711524, … |
| maximal normal subgroup of | #11711520, #11711523, #11711524, … |
| maximal quotient of | #11711068, #11711069, #11711074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5696);