Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #137 |
180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 22 points:
(2,7)(3,10)(4,12)(6,13)(8,9)(14,15)(20,21,22);(1,3)(2,6)(4,11)(5,10)(7,15)(8,13)(9,14)(12,16)(17,18,19);(1,2,5,9)(3,6,10,14)(4,7,12,8)(11,15,16,13)(18,19)(21,22)Polycyclic presentation:
2^5,3^2|a^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^2,g^a=g^2,c^b=ce,d^c=de51 conjugacy classes — view the full character table.
| maximal subgroup of | #10591679, #10591682, #10591688, … |
| maximal normal subgroup of | #10591679, #10591682, #10591688, … |
| maximal quotient of | #10592694, #10592695, #10592703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 808);