Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C9 ⋊ #117 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,6,8,7,2,4,3,9,5)(15,19)(18,21);(14,16,17,20)(15,18,19,21);(2,4)(3,7)(5,6)(8,9)(10,11,12,13)(14,15)(16,18)(17,19)(20,21)Polycyclic presentation:
2^5,3^2|a^2=d,b^2=e,f^3=g^2,c^a=ce,f^a=f^2g,g^a=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10588201, #10588210, #10588232, … |
| maximal normal subgroup of | #10588201, #10588210, #10588232, … |
| maximal quotient of | #10588605, #10588606, #10588612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 136);