Finite Group Databasebeta

← Prev (#34062382) Next (#34062384) →

C11×C3⋊#10596816 #34062383

order19140
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊#10596816
unambiguous semidirect productC3⋊(C11×#10596816)

Splittings

Fitting, socle, HallC3×C5×C11×C29 ⋊ C4
derived, HallC3×C5×C29 ⋊ C4×C11
HallC5×C11×C29 ⋊ Dic3
HallC3×C11×C29 ⋊ AGL(1,𝔽5)
HallC11×C29 ⋊ ΓL(1,𝔽16)
HallC3×C5×C11 ⋊ Dic29
HallC5×C29 ⋊ C11×Dic3
HallC3×C29 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ Dic87
HallC3×C11 ⋊ #10596816
SylowC29 ⋊ C11×ΓL(1,𝔽16)
HallC3×C5 ⋊ C11×Dic29
SylowC5 ⋊ C11×Dic87
SylowC3 ⋊ C11×#10596816

Subgroups

subgroupG/H
center, hypercenterC11C3⋊#10596816
commutator, hypocenterC3×C5×C29C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C29C4
prime radicalC3×D5×C11×C29C2
cosocleC3×D5×C29C2×C11
LCSG ▷ C3×C5×C29
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

1947 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 76);