Finite Group Databasebeta

← Prev (#34062328) Next (#34062330) →

C11⋊C5×Dic87 #34062329

order19140
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×Dic87
unambiguous semidirect productC3⋊(C11⋊C5×Dic29)
unambiguous semidirect product(C11×Dic87)⋊C5

Splittings

derived, HallC3×C11×C29 ⋊ C4×C5
HallC3×C29×C11⋊C5 ⋊ C4
HallC11×Dic87 ⋊ C5
HallC29×C11⋊C5 ⋊ Dic3
HallC11×C29 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ Dic29
HallC3×C29 ⋊ C4×C11⋊C5
HallC3×C11 ⋊ C5×Dic29
SylowC29 ⋊ Dic3×C11⋊C5
SylowC11 ⋊ C5×Dic87
SylowC3 ⋊ C11⋊C5×Dic29

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×D87
commutator, hypocenterC3×C11×C29C4×C5
Fitting, socle, cosocleC2×C3×C11×C29C2×C5
prime radicalC2×C3×C29×C11⋊C5C2
LCSG ▷ C3×C11×C29
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3828

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 22);