Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #117 |
165 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,3,4)(6,10)(9,12)(13,14,15)(16,17,18);(5,7,8,11)(6,9,10,12)(14,15);(5,6)(7,9)(8,10)(11,12)(17,18)Polycyclic presentation:
2^5,3^2|b^2=e,c^2=d,c^a=ce,g^a=g^2,f^b=f^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10593885, C4×#3795, #10593889, … |
| maximal normal subgroup of | #10593885, C4×#3795, #10593889, … |
| maximal quotient of | #10590655, #10590660, #10590696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 525);