Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C32×Q8 ⋊ C4 |
| Sylow | C32 ⋊ #104 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,3,6)(2,5,4)(7,9,12,8)(10,14,11,13);(1,2)(3,5,6,4)(7,8,10,13,12,9,11,14)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=e,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=fg^2,g^a=f^2g^2,d^b=de,f^c=f^2,g^c=g^224 conjugacy classes — view the full character table.
| maximal subgroup of | #10593473, #10593475, #10593483, … |
| maximal normal subgroup of | #10593473, #10593475, #10593483, … |
| maximal quotient of | #10590157, #10590159, #10590160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 433);