Finite Group DatabasebetaFinite Group Databasebeta| order | 507 |
| isoclinism | isoclinic class of #92788 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C132 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132 | C3 |
| LCS | G ▷ C132 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 169 |
A minimal faithful permutation representation — 3 generators on 26 points:
(2,3,5)(4,7,10)(6,9,8)(11,13,12)(15,16,18)(17,20,23)(19,22,21)(24,26,25);(14,15,17,16,19,23,20,24,26,18,21,25,22);(1,2,4,3,6,10,7,11,13,5,8,12,9)Polycyclic presentation:
3,13^2|b^a=b^3,c^a=c^359 conjugacy classes — view the full character table.
| maximal subgroup of | #11759815, #11759817, C2×#92788, … |
| maximal normal subgroup of | #11759815, #11759817, C2×#92788, … |
| maximal quotient of | C2×#92788, #13095200, C3×#92788, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(507, 4);