Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #63745 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #106 |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,4,5,6)(3,8,7,9)(11,15)(12,13)(16,17);(2,4,5,9)(3,7,8,6)(10,11,12,15,14,17,13,16)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=cd,c^2=e,d^2=e,b^a=bce,f^a=fg^2,g^a=f^2g^2,c^b=ce,d^b=de,f^b=g,g^b=f^2,f^c=f^2,g^c=g^218 conjugacy classes — view the full character table.
| maximal subgroup of | #10593162, #10593163, #10593534, … |
| maximal normal subgroup of | #10593162, #10593163, #10593534, … |
| maximal quotient of | #10590084, #10590088, #10590093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 393);