Finite Group Databasebeta

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C2×C11×C25×D19 #35229854

order20900
automorphism?
homologyAbelianization (H1) = C22×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C25×D19
unambiguous semidirect productC19⋊(C22×C11×C25)
unambiguous semidirect product(C2×C19)⋊(C2×C11×C25)

Splittings

FittingC2×C11×C19×C25 ⋊ C2
derived, SylowC19 ⋊ C22×C11×C25
HallC11×C19×C25 ⋊ C22
HallC19×C25 ⋊ C22×C11
HallC11×C19 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C11×C25D19
commutator, hypocenterC19C22×C11×C25
FrattiniC5C2×C5×C11×D19
FittingC2×C11×C19×C25C2
socleC2×C5×C11×C19C2×C5
prime radicalC2×C5×C11×D19C5
cosocleC5×C19C22×C5×C11
LCSG ▷ C19
UCSC1 ◁ C2×C11×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10450

Conjugacy classes & character table

6050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 36);