Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #97 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 288 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,6,8,7,2,4,3,9,5)(14,15,16,19,17,18,20,21);(2,4)(3,7)(5,6)(8,9)(10,11,12,13)(15,18)(19,21)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=d,d^2=e,f^3=g^2,b^a=be,f^a=f^2g,g^a=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10588189, #10588359, C4×#3663, … |
| maximal normal subgroup of | #10588189, #10588359, C4×#3663, … |
| maximal quotient of | #10588131, #10588132, #10588189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 23);