Finite Group Databasebeta

← Prev (#44535499) Next (#44535501) →

C11×(C5⋊D5)⋊(C19⋊C3) #44535500

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×(C5⋊D5)⋊(C19⋊C3)
unambiguous semidirect product(C5⋊D5)⋊(C11×C19⋊C3)
unambiguous semidirect product(C11×C5⋊D5)⋊(C19⋊C3)

Splittings

Fitting, socle, HallC52×C11×C19 ⋊ C2×C3
derived, HallC52×C19 ⋊ C2×C3×C11
HallC11×C19⋊(C52⋊C3) ⋊ C2
HallC11×C19×C5⋊D5 ⋊ C3
HallC19⋊(C52⋊C3) ⋊ C2×C11
HallC19×C5⋊D5 ⋊ C3×C11
HallC11×C5⋊D5 ⋊ C19⋊C3
HallC52×C11 ⋊ C2×C19⋊C3
HallC11×C19 ⋊ (C5⋊D5)⋊C3
HallC5⋊D5 ⋊ C11×C19⋊C3
SylowC52 ⋊ C2×C11×C19⋊C3
SylowC19 ⋊ C11×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC11(C5⋊D5)⋊(C19⋊C3)
commutator, cosocle, hypocenterC52×C19C2×C3×C11
FrattiniC1G
Fitting, socleC52×C11×C19C2×C3
LCSG ▷ C52×C19
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

1034 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 73);