Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ C2×SD16 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,3,4)(2,5,6)(7,9,11,10)(8,13,14,12);(3,4)(7,8,11,14)(9,12,10,13);(1,2)(3,6)(4,5)(8,12)(9,10)(13,14)Polycyclic presentation:
2^5,3^2|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 | #10593290, #10593291, #10593292, … |
| maximal normal subgroup of | #10593290, #10593291, #10593292, … |
| maximal quotient of | #10593348, #10593354, #10593355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 875);