Finite Group Databasebeta

← Prev (#35229832) Next (#35229834) →

C2×C19×D11⋊C25 #35229833

order20900
automorphism?
homologyAbelianization (H1) = C22×C19×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C19×D11⋊C25
unambiguous semidirect productD11⋊(C2×C19×C25)
unambiguous semidirect product(C2×D11)⋊(C19×C25)
unambiguous semidirect product(C11⋊C25)⋊(C22×C19)
unambiguous semidirect product(C2×C11⋊C25)⋊(C2×C19)
unambiguous semidirect product(C2×C19×D11)⋊C25

Splittings

derived, SylowC11 ⋊ C22×C19×C25
HallC19×C11⋊C25 ⋊ C22
HallC2×C19×D11 ⋊ C25
HallC11⋊C25 ⋊ C22×C19
HallC11×C19 ⋊ C22×C25
HallC2×D11 ⋊ C19×C25

Subgroups

subgroupG/H
center, hypercenterC2×C5×C19AGL(1,𝔽11)
commutator, hypocenterC11C22×C19×C25
FrattiniC5C2×C19×AGL(1,𝔽11)
Fitting, socleC2×C5×C11×C19C2×C5
prime radicalC2×C5×C19×D11C5
cosocleC5×C11C22×C5×C19
LCSG ▷ C11
UCSC1 ◁ C2×C5×C19

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10450

Conjugacy classes & character table

2090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 15);