Finite Group DatabasebetaFinite Group Databasebeta| order | 2310 |
| isoclinism | isoclinic class of D5×ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | D5×C11×ΓL(1,𝔽8) |
| unambiguous semidirect product | C5⋊(C2×C11×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×D5)⋊(C3×C11) |
| unambiguous semidirect product | (C7×D5×C11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D5×ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C5×C7 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C11 | C2×C3 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C11 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 385 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(18,19,20)(21,23,22);(2,5)(3,4)(17,18,19,21,20,22,23)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2310, 30);