Finite Group DatabasebetaFinite Group Databasebeta| order | 465 |
| isoclinism | isoclinic class of (C31⋊C3)⋊C5 |
| automorphism | Aut(G) = AGL(1,𝔽31) (order 930) · Inn(G) = G · Out(G) = C2 |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C3)⋊C5 |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊C3 |
| Fitting, socle, derived, Sylow | C31 ⋊ C3×C5 |
| Hall | ΓL(1,𝔽32) ⋊ C3 |
| Hall | C31⋊C3 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31 | C3×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 31 |
A minimal faithful permutation representation — 2 generators on 31 points:
(2,7,21,20,11,6,4,15,25,5,3,13,9,26,24)(8,27,10,30,16,14,18,29,23,31,17,12,22,19,28);(1,2,5,12,20,6,14,26,9,21,24,30,28,18,15,27,4,10,13,11,25,31,22,29,23,3,8,19,7,16,17)Polycyclic presentation:
3,5,31|c^a=c^25,c^b=c^1617 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(465, 1);