Finite Group DatabasebetaFinite Group Databasebeta| order | 3990 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C5×C19×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C3×C5×C19) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C2×C5×C19) |
| unambiguous semidirect product | (C5×D7)⋊(C3×C19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C7 | C2×C3×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C19 | C2×C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C5×C19 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 665 |
A minimal faithful permutation representation — 2 generators on 31 points:
(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24)(26,29,30,27,28,31);(25,26,28,31,30,29,27)665 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3990, 26);