Finite Group Databasebeta

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C5×D19×AGL(1,𝔽11) #35229876

order20900
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC5×D19×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C52×D19)
unambiguous semidirect product(D11×D19)⋊C52
unambiguous semidirect product(D19×C11⋊C5)⋊(C2×C5)
unambiguous semidirect product(C19×AGL(1,𝔽11))⋊(C2×C5)
unambiguous semidirect product(C19⋊AGL(1,𝔽11))⋊(C2×C5)
unambiguous semidirect product(C5×D11×D19)⋊C5

Splittings

Fitting, socleC5×C11×C19 ⋊ C22×C5
derived, HallC11×C19 ⋊ C22×C52
HallC5×C19×C11⋊C5 ⋊ C22
HallD11×D19 ⋊ C52
HallC5×C11⋊C5 ⋊ C2×D19
SylowC19 ⋊ C2×C5×AGL(1,𝔽11)
SylowC11 ⋊ C2×C52×D19

Subgroups

subgroupG/H
center, hypercenterC5D19×AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C19C22×C52
FrattiniC1G
Fitting, socleC5×C11×C19C22×C5
LCSG ▷ C11×C19
UCSC1 ◁ C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1045

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 58);