Finite Group Databasebeta

← Prev (#44526655) Next (#44526657) →

C11×C47×ΓL(1,𝔽16) #44526656

order31020
automorphism?
homologyAbelianization (H1) = C4×C11×C47 · Schur multiplier (H2) = C1

Aliases

direct productC11×C47×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C11×AGL(1,𝔽5)×C47)

Splittings

Fitting, socle, HallC3×C5×C11×C47 ⋊ C4
derived, HallC3×C5 ⋊ C4×C11×C47
HallC5×C11×C47 ⋊ Dic3
HallC3×C11×C47 ⋊ AGL(1,𝔽5)
HallC3×C5×C47 ⋊ C4×C11
HallC5×C47 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ C4×C47
HallC3×C47 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ Dic3×C47
HallC3×C11 ⋊ AGL(1,𝔽5)×C47
SylowC5 ⋊ C11×Dic3×C47
SylowC3 ⋊ C11×AGL(1,𝔽5)×C47

Subgroups

subgroupG/H
center, hypercenterC11×C47ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C11×C47
FrattiniC1G
Fitting, socleC3×C5×C11×C47C4
prime radicalC3×D5×C11×C47C2
cosocleC3×D5C2×C11×C47
LCSG ▷ C3×C5
UCSC1 ◁ C11×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7755

Conjugacy classes & character table

4653 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 59);