Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of Dic36 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #103 |
63 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 288 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,5,7,9,8,3,6,4)(10,12,13,11)(14,15,16,18,17,19,20,21);(2,4)(3,7)(5,6)(8,9)(10,11,13,12)(15,18)(16,20)(19,21)Polycyclic presentation:
2^5,3^2|a^2=d,b^2=cd,c^2=e,f^3=g^2,b^a=bc,c^a=ce,f^a=f^2g,g^a=g^278 conjugacy classes — view the full character table.
| maximal subgroup of | #10588361, C4×Dic36, C4×#3664, … |
| maximal normal subgroup of | #10588361, C4×Dic36, C4×#3664, … |
| maximal quotient of | #10588133, #10588144, #10588158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 24);