Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #101 |
57 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,6,8,7,2,4,3,9,5)(10,12,14,20)(11,15,17,18)(13,21,22,19)(16,24,25,23);(2,4)(3,7)(5,6)(8,9)(10,11,13,16,14,17,22,25)(12,18,19,24,20,15,21,23)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=e,c^2=e,f^3=g^2,b^a=bd,d^a=de,f^a=f^2g,g^a=g^2,c^b=ce51 conjugacy classes — view the full character table.
| maximal subgroup of | #10588154, #10588155, #10588219, … |
| maximal normal subgroup of | #10588154, #10588155, #10588219, … |
| maximal quotient of | #10588205, #10588207, #10588220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 42);