Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #100 |
119 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 14 points:
(2,3)(4,5,6)(7,9,10,13,11,12,14,8);(1,2,3)(5,6)(7,8,10,12,11,13,14,9)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=cd,c^2=e,b^a=bd,d^a=de,g^a=g^2,c^b=ce,d^b=de,f^b=f^239 conjugacy classes — view the full character table.
| maximal subgroup of | #10590057, #10590058, #10590397, … |
| maximal normal subgroup of | #10590057, #10590058, #10590397, … |
| maximal quotient of | #10589087, #10589091, #10589096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 207);