Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #101 |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 22 points:
(2,3)(4,5,6)(7,9,10,16,11,17,19,22)(8,12,13,20,14,15,18,21);(1,2,3)(5,6)(7,8,11,14)(9,15,17,12)(10,18,19,13)(16,20,22,21)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=c,c^2=e,b^a=bd,c^a=ce,g^a=g^2,d^b=de,f^b=f^239 conjugacy classes — view the full character table.
| maximal subgroup of | #10590399, #10590400, #10590925, … |
| maximal normal subgroup of | #10590399, #10590400, #10590925, … |
| maximal quotient of | #10589088, #10589092, #10589093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 208);