Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #103 |
126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 288 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,3,4)(6,9)(7,12)(10,11)(16,17,18);(5,6,8,11)(7,9,12,10)(14,15)(17,18);(13,14,15)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=c,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^2,d^b=de54 conjugacy classes — view the full character table.
| maximal subgroup of | #10590426, #10590427, #10590428, … |
| maximal normal subgroup of | #10590426, #10590427, #10590428, … |
| maximal quotient of | #10589318, #10589347, #10589350, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 285);