Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,2,4)(5,7,16,32,9,18,22,24,10,19,27,36,21,33,8,17)(6,11,20,30,13,25,28,31,14,26,35,34,23,29,12,15);(2,3)(5,6,10,14)(7,15,19,31)(8,20,22,35)(9,23,21,13)(11,24,26,17)(12,27,28,16)(18,34,33,30)(25,32,29,36)Polycyclic presentation:
2^5,3,2^2|a^2=e,b^2=cd,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=h,h^a=g,g^f=h,h^f=gh38 conjugacy classes — view the full character table.
| maximal subgroup of | #11711664, #11711665, #11711676, … |
| maximal normal subgroup of | #11711664, #11711665, #11711676, … |
| maximal quotient of | #11711471, #11711474, #11711478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5613);