Finite Group DatabasebetaFinite Group Databasebeta| order | 2310 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C11⋊C5)⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (C11⋊AGL(1,𝔽7))⋊C5 |
| unambiguous semidirect product | (C7⋊AGL(1,𝔽11))⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11 | C2×C3×C5 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 77 |
Polycyclic presentation:
2,3,5,7,11|d^a=d^6,e^a=e^10,d^b=d^2,e^c=e^440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2310, 36);