Finite Group Databasebeta

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C11×C11⋊C5×C19⋊C3 #46828437

order34485
automorphism?
homologyAbelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C11⋊C5×C19⋊C3
unambiguous semidirect productC11⋊(C5×C11×C19⋊C3)
unambiguous semidirect productC19⋊(C3×C11×C11⋊C5)
unambiguous semidirect product(C11×C19⋊C3)⋊(C5×C11)
unambiguous semidirect product(C19×C11⋊C5)⋊(C3×C11)
unambiguous semidirect product(C11×C19×C11⋊C5)⋊C3

Splittings

Fitting, socle, HallC112×C19 ⋊ C3×C5
derivedC11×C19 ⋊ C3×C5×C11
HallC11×C19×C11⋊C5 ⋊ C3
HallC112×C19⋊C3 ⋊ C5
SylowC112 ⋊ C5×C19⋊C3
SylowC19 ⋊ C3×C11×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC11C11⋊C5×C19⋊C3
commutator, cosocle, hypocenterC11×C19C3×C5×C11
FrattiniC1G
Fitting, socleC112×C19C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C11

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1045

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34485, 8);