Finite Group Databasebeta

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C3×C19⋊(D11⋊C25) #44535449

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19⋊(D11⋊C25)
unambiguous semidirect product(C11⋊C25)⋊(C3×D19)
unambiguous semidirect product(C3×D209)⋊C25

Splittings

derived, HallC11×C19 ⋊ C2×C3×C25
HallC3×C19×C11⋊C25 ⋊ C2
HallC19×C11⋊C25 ⋊ C2×C3
HallC3×D209 ⋊ C25
HallC3×C11⋊C25 ⋊ D19
HallC3×C11×C19 ⋊ C2×C25
HallD209 ⋊ C3×C25
HallC11⋊C25 ⋊ C3×D19
HallC3×C19 ⋊ D11⋊C25
HallC3×C11 ⋊ C25×D19
SylowC19 ⋊ C3×D11⋊C25
SylowC11 ⋊ C3×C25×D19

Subgroups

subgroupG/H
center, hypercenterC3×C5C19⋊AGL(1,𝔽11)
commutator, hypocenterC11×C19C2×C3×C25
FrattiniC5C3×C19⋊AGL(1,𝔽11)
Fitting, socleC3×C5×C11×C19C2×C5
prime radicalC3×C5×D209C5
cosocleC5×C11×C19C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

1110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 22);