Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #101 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,3,6)(2,5,4)(7,9,11,17)(8,12,14,15)(10,18,19,16)(13,21,22,20);(1,2)(3,5,6,4)(7,8,10,13,11,14,19,22)(9,15,16,21,17,12,18,20)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=e,c^2=e,b^a=bd,d^a=de,f^a=fg^2,g^a=f^2g^2,c^b=ce,f^c=f^2,g^c=g^227 conjugacy classes — view the full character table.
| maximal subgroup of | #10590059, #10590060, #10590144, … |
| maximal normal subgroup of | #10590059, #10590060, #10590144, … |
| maximal quotient of | #10590159, #10590162, #10590202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 428);