Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ C2×M16 |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,3,6)(2,5,4)(8,13)(12,14);(7,9,11,10)(8,12,13,14);(1,2)(3,5,6,4)(7,8,10,14,11,13,9,12)Polycyclic presentation:
2^5,3^2|a^2=d,b^2=e,d^2=e,c^a=ce,f^a=fg^2,g^a=f^2g^2,f^d=f^2,g^d=g^236 conjugacy classes — view the full character table.
| maximal subgroup of | #10590050, #10590054, #10590056, … |
| maximal normal subgroup of | #10590050, #10590054, #10590056, … |
| maximal quotient of | #10593723, C4×#3788, #10593725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 931);