Finite Group Databasebeta

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D5×C11×D133 #44418005

order29260
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productD5×C11×D133
unambiguous semidirect product(C7×D5)⋊(C11×D19)
unambiguous semidirect product(D5×C19)⋊(C11×D7)

Splittings

Fitting, socle, HallC5×C7×C11×C19 ⋊ C22
derived, HallC5×C7×C19 ⋊ C22×C11
HallC7×C11×C19 ⋊ C2×D5
HallC5×C11×C19 ⋊ C2×D7
HallC5×C7×C11 ⋊ C2×D19
HallC11×C19 ⋊ D5×D7
HallC7×C19 ⋊ C2×D5×C11
HallC5×C19 ⋊ C2×C11×D7
HallC7×C11 ⋊ D5×D19
HallC5×C11 ⋊ C2×D133
HallC5×C7 ⋊ C2×C11×D19
SylowC19 ⋊ D5×C11×D7
SylowC7 ⋊ D5×C11×D19
SylowC5 ⋊ C2×C11×D133

Subgroups

subgroupG/H
center, hypercenterC11D5×D133
commutator, cosocle, hypocenterC5×C7×C19C22×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C19C22
LCSG ▷ C5×C7×C19
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7315

Conjugacy classes & character table

2992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29260, 70);