Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #137 |
130 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 130 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:
(1,4,6,5)(2,8,9,14)(3,11,13,12)(7,10,15,16)(17,18,19)(20,21,22);(1,3,6,13)(2,7,9,15)(4,12,5,11)(8,16,14,10)(18,19);(1,2)(3,10)(4,8)(5,14)(6,9)(7,12)(11,15)(13,16)(21,22)Polycyclic presentation:
2^5,3^2|b^2=e,c^2=e,d^2=e,b^a=bd,d^a=de,g^a=g^2,c^b=ce,d^b=de,f^b=f^239 conjugacy classes — view the full character table.
| maximal subgroup of | #10590396, #10590399, #10590925, … |
| maximal normal subgroup of | #10590396, #10590399, #10590925, … |
| maximal quotient of | #10590267, #10590269, #10590280, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 475);