Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ C2×Q16 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,3,4)(2,5,6)(7,10,12,11)(8,14,16,15)(9,18,20,19)(13,21,22,17);(3,4)(7,9,12,20)(8,13,16,22)(10,19,11,18)(14,17,15,21);(1,2)(3,6)(4,5)(7,8,12,16)(9,17,20,21)(10,15,11,14)(13,18,22,19)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=e,c^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^2,c^b=ce,d^b=de,f^b=g,g^b=f,f^d=f^2,g^d=g^224 conjugacy classes — view the full character table.
| maximal subgroup of | #10593161, #10593291, #10593295, … |
| maximal normal subgroup of | #10593161, #10593291, #10593295, … |
| maximal quotient of | #10593371, #10593372, #10593375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 876);