Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3713 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#3715 |
| Sylow | C32 ⋊ C2×SD16 |
147 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 147 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2)(4,5)(6,7,8)(9,10,12,14)(11,16,15,13);(3,4,5)(7,8)(10,13)(11,15)(14,16);(1,2)42 conjugacy classes — view the full character table.
| maximal subgroup of | #10590267, #10590348, #10590353, … |
| maximal normal subgroup of | #10590267, #10590348, #10590353, … |
| maximal quotient of | #10590266, #10590277, #10590285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 474);