Finite Group Databasebeta

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C7×D5×C19×D11 #44417993

order29260
automorphism?
homologyAbelianization (H1) = C22×C7×C19 · Schur multiplier (H2) = C2

Aliases

direct productC7×D5×C19×D11
unambiguous semidirect product(D5×C11)⋊(C2×C7×C19)
unambiguous semidirect product(C5×D11)⋊(C2×C7×C19)
unambiguous semidirect productD55⋊(C2×C7×C19)

Splittings

Fitting, socle, HallC5×C7×C11×C19 ⋊ C22
derived, HallC5×C11 ⋊ C22×C7×C19
HallC7×C11×C19 ⋊ C2×D5
HallC5×C11×C19 ⋊ C22×C7
HallC5×C7×C19 ⋊ C2×D11
HallC5×C7×C11 ⋊ C22×C19
HallC11×C19 ⋊ C2×C7×D5
HallC5×C19 ⋊ C2×C7×D11
HallC7×C11 ⋊ C2×D5×C19
HallC5×C7 ⋊ C2×C19×D11
SylowC11 ⋊ C2×C7×D5×C19
SylowC5 ⋊ C2×C7×C19×D11

Subgroups

subgroupG/H
center, hypercenterC7×C19D5×D11
commutator, cosocle, hypocenterC5×C11C22×C7×C19
FrattiniC1G
Fitting, socleC5×C7×C11×C19C22
LCSG ▷ C5×C11
UCSC1 ◁ C7×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7315

Conjugacy classes & character table

3724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29260, 58);