Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ C4×D4 |
215 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 215 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(5,6,7,8)(9,10,11)(12,13,14);(1,3,4,2)(6,8)(10,11);(1,2,4,3)(13,14)Polycyclic presentation:
2^5,3^2|a^2=d,b^2=d,c^2=e,g^a=g^2,c^b=ce,f^b=f^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10590456, #10590457, #10590458, … |
| maximal normal subgroup of | #10590456, #10590457, #10590458, … |
| maximal quotient of | #10590327, #10590328, #10590338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 542);