Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3713 |
| automorphism | Aut(G) = C22×D32×D4 (order 1152) · Inn(G) = #625 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #104 |
103 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,3,4,2,5,6,8,7)(10,11)(12,13,14);(1,2)(3,8)(4,6)(5,7)(9,10,11)(13,14)Polycyclic presentation:
2^5,3^2|b^2=c,c^2=e,d^2=e,b^a=bd,d^a=de,g^a=g^2,d^b=de,f^b=f^242 conjugacy classes — view the full character table.
| maximal subgroup of | #10590393, #10590394, #10590919, … |
| maximal normal subgroup of | #10590393, #10590394, #10590919, … |
| maximal quotient of | #10589080, #10589083, #10589086, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 216);