Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C9×C4⋊C4 ⋊ C2 |
| Sylow | C9 ⋊ #102 |
75 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,5,7,9,8,3,6,4)(10,11,12,13)(15,18)(16,21)(19,20);(2,4)(3,7)(5,6)(8,9)(14,15)(16,18)(17,20)(19,21)Polycyclic presentation:
2^5,3^2|b^2=c,d^2=e,f^3=g^2,b^a=bd,d^a=de,f^a=f^2g,g^a=g^2,d^b=de54 conjugacy classes — view the full character table.
| maximal subgroup of | #10588440, #10588442, #10588444, … |
| maximal normal subgroup of | #10588440, #10588442, #10588444, … |
| maximal quotient of | #10588129, #10588159, #10588162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 17);