Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #137 |
140 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 22 points:
(3,10)(6,15)(9,16)(11,14)(17,18,19)(20,21,22);(1,3,4,11,5,10,13,14)(2,6,7,9,8,15,12,16)(18,19);(1,2,5,8)(3,9,10,16)(4,12,13,7)(6,14,15,11)(21,22)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=d,d^2=e,b^a=bd,d^a=de,g^a=g^2,c^b=ce,f^b=f^239 conjugacy classes — view the full character table.
| maximal subgroup of | #10590396, #10590399, #10590928, … |
| maximal normal subgroup of | #10590396, #10590399, #10590928, … |
| maximal quotient of | #10590289, #10590294, #10590302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 481);