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 |
203 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 203 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 96 |
A minimal faithful permutation representation — 3 generators on 14 points:
(5,6,7,8)(9,10,11)(12,13,14);(1,2,3,4)(6,8)(10,11);(6,8)(13,14)Polycyclic presentation:
2^5,3^2|b^2=d,c^2=e,c^a=ce,g^a=g^2,c^b=ce,f^b=f^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10590459, #10590460, #10590461, … |
| maximal normal subgroup of | #10590459, #10590460, #10590461, … |
| maximal quotient of | #10590329, #10590330, #10590339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 546);