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)(10,12,13,19,14,20,22,25)(11,15,16,23,17,18,21,24);(2,4)(3,7)(5,6)(8,9)(10,11,14,17)(12,18,20,15)(13,21,22,16)(19,23,25,24)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=c,c^2=e,f^3=g^2,b^a=bd,c^a=ce,f^a=f^2g,g^a=g^2,d^b=de51 conjugacy classes — view the full character table.
| maximal subgroup of | #10588425, #10588428, D9×#101, … |
| maximal normal subgroup of | #10588425, #10588428, D9×#101, … |
| maximal quotient of | #10588141, #10588145, #10588159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 30);