Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ C2×C4⋊C4 |
211 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2,3,4)(5,6)(7,8)(9,10,11)(12,13,14);(5,6,7,8)(10,11);(5,6,7,8)(13,14)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=e,c^2=d,c^a=ce,g^a=g^2,c^b=ce,f^b=f^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10590028, #10593338, #10593339, … |
| maximal normal subgroup of | #10590028, #10593338, #10593339, … |
| maximal quotient of | #10590573, #10590574, #10590575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 531);