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C7×D19×D55 #44417992

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

Aliases

direct productC7×D19×D55
unambiguous semidirect product(C5×D19)⋊(C7×D11)
unambiguous semidirect product(C11×D19)⋊(C7×D5)

Splittings

Fitting, socle, HallC5×C7×C11×C19 ⋊ C22
derived, HallC5×C11×C19 ⋊ C22×C7
HallC7×C11×C19 ⋊ C2×D5
HallC5×C7×C19 ⋊ C2×D11
HallC5×C7×C11 ⋊ C2×D19
HallC11×C19 ⋊ C2×C7×D5
HallC7×C19 ⋊ C2×D55
HallC5×C19 ⋊ C2×C7×D11
HallC7×C11 ⋊ D5×D19
HallC5×C11 ⋊ C2×C7×D19
HallC5×C7 ⋊ D11×D19
SylowC19 ⋊ C2×C7×D55
SylowC11 ⋊ C7×D5×D19
SylowC5 ⋊ C7×D11×D19

Subgroups

subgroupG/H
center, hypercenterC7D19×D55
commutator, cosocle, hypocenterC5×C11×C19C22×C7
FrattiniC1G
Fitting, socleC5×C7×C11×C19C22
LCSG ▷ C5×C11×C19
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7315

Conjugacy classes & character table

2233 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29260, 57);