Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #63626 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C32 ⋊ Q32 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 288 |
A minimal faithful permutation representation — 3 generators on 38 points:
(1,3,12,28,5,14,18,20,6,15,23,32,17,29,4,13)(2,7,16,26,9,21,24,27,10,22,31,30,19,25,8,11)(36,37,38);(1,2,6,10)(3,11,15,27)(4,16,18,31)(5,19,17,9)(7,20,22,13)(8,23,24,12)(14,30,29,26)(21,28,25,32)(34,35)(37,38);(33,34,35)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=cd,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=g^275 conjugacy classes — view the full character table.
| maximal subgroup of | #10589073, #10589076, #10589315, … |
| maximal normal subgroup of | #10589073, #10589076, #10589315, … |
| maximal quotient of | #10589369, #10589370, C2×#63628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 276);