Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3713 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C32 ⋊ #108 |
71 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,3,4,11,6,12,5,14)(2,7,8,15,9,16,13,10)(18,19)(20,21,22);(1,2,4,8,6,9,5,13)(3,10,11,7,12,15,14,16)(17,18,19)(21,22)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=c,c^2=e,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 | #10590063, #10590065, #10590066, … |
| maximal normal subgroup of | #10590063, #10590065, #10590066, … |
| maximal quotient of | #10589098, #10589100, #10589165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 226);