Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q8×C9 ⋊ C2 |
| Sylow | C9 ⋊ #137 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,5,7,9,8,3,6,4)(10,13,15,22)(11,17,18,25)(12,19,14,21)(16,24,23,20);(10,12,15,14)(11,16,18,23)(13,21,22,19)(17,20,25,24);(2,4)(3,7)(5,6)(8,9)(10,11)(12,16)(13,20)(14,23)(15,18)(17,19)(21,25)(22,24)Polycyclic presentation:
2^5,3^2|b^2=e,c^2=e,d^2=e,f^3=g^2,c^a=cd,d^a=de,f^a=f^2g,g^a=g^2,c^b=ce,d^c=de51 conjugacy classes — view the full character table.
| maximal subgroup of | #10588434, #10588435, #10588741, … |
| maximal normal subgroup of | #10588434, #10588435, #10588741, … |
| maximal quotient of | #10588644, #10588647, #10588649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 153);