Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of Dic36 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C9 ⋊ #108 |
45 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,5,7,9,8,3,6,4)(10,12,14,21,15,22,13,20)(11,16,17,19,18,24,23,25);(2,4)(3,7)(5,6)(8,9)(10,11,13,17,15,18,14,23)(12,19,20,24,22,25,21,16)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=d,c^2=e,d^2=e,f^3=g^2,b^a=bd,d^a=de,f^a=f^2g,g^a=g^278 conjugacy classes — view the full character table.
| maximal subgroup of | #10588164, #10588170, #10588183, … |
| maximal normal subgroup of | #10588164, #10588170, #10588183, … |
| maximal quotient of | #10588134, #10588135, #10588227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 20);