Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ C2×Q16 |
131 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,4,13,16,6,15,5,14)(2,7,10,12,3,9,8,11)(17,18,19)(20,21,22);(1,3,6,2)(4,12,15,11)(5,8,13,10)(7,14,9,16)(18,19);(1,2,6,3)(4,11,15,12)(5,10,13,8)(7,16,9,14)(21,22)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=e,c^2=de,d^2=e,c^a=cd,d^a=de,g^a=g^2,c^b=cd,d^b=de,f^b=f^236 conjugacy classes — view the full character table.
| maximal subgroup of | #10590017, #10590021, #10590235, … |
| maximal normal subgroup of | #10590017, #10590021, #10590235, … |
| maximal quotient of | #10590672, #10590687, #10590689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 450);