Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3713 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #102 |
111 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,3,4)(6,9)(7,12)(10,11)(14,15)(16,17,18);(5,6)(7,9)(8,11)(10,12)(13,14,15)(17,18)Polycyclic presentation:
2^5,3^2|b^2=c,d^2=e,b^a=bd,d^a=de,g^a=g^2,d^b=de,f^b=f^242 conjugacy classes — view the full character table.
| maximal subgroup of | #10590266, #10590267, #10590269, … |
| maximal normal subgroup of | #10590266, #10590267, #10590269, … |
| maximal quotient of | #10589080, #10589090, #10589093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 210);