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C19×(C11⋊C5)⋊AGL(1,𝔽5) #35229877

order20900
automorphism?
homologyAbelianization (H1) = C4×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×(C11⋊C5)⋊AGL(1,𝔽5)
unambiguous semidirect product(C11⋊C5)⋊(C19×AGL(1,𝔽5))
unambiguous semidirect product(C11⋊AGL(1,𝔽5))⋊(C5×C19)
unambiguous semidirect product(C19×C11⋊AGL(1,𝔽5))⋊C5

Splittings

Fitting, socleC5×C11×C19 ⋊ C4×C5
derivedC5×C11 ⋊ C4×C5×C19
HallC5×C19×C11⋊C5 ⋊ C4
HallC5×C11⋊C5 ⋊ C4×C19
HallC11×C19 ⋊ C5×AGL(1,𝔽5)
SylowC11 ⋊ C5×C19×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC19(C11⋊C5)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C5×C19
FrattiniC1G
Fitting, socleC5×C11×C19C4×C5
prime radicalD5×C19×C11⋊C5C2
cosocleD5×C11C2×C5×C19
LCSG ▷ C5×C11
UCSC1 ◁ C19

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1045

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 59);