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 68 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 68 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:
(5,8,9,7)(6,10,11,12)(13,14,15)(16,17,18);(5,7,9,8)(6,10,11,12)(14,15);(1,2,3,4)(5,6)(7,10)(8,12)(9,11)(17,18)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=d,c^2=d,c^a=cd,g^a=g^2,f^b=f^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10590446, #10590447, #10590448, … |
| maximal normal subgroup of | #10590446, #10590447, #10590448, … |
| maximal quotient of | #10590248, #10590253, #10590263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 489);