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C2×C13×D121⋊C5 #44538077

order31460
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D121⋊C5
unambiguous semidirect productD121⋊(C2×C5×C13)
unambiguous semidirect product(C2×D121)⋊(C5×C13)
unambiguous semidirect product(C121⋊C5)⋊(C22×C13)
unambiguous semidirect product(C2×C121⋊C5)⋊(C2×C13)
unambiguous semidirect product(C2×C13×D121)⋊C5

Splittings

FittingC2×C13×C121 ⋊ C2×C5
derived, SylowC121 ⋊ C22×C5×C13
HallC13×C121⋊C5 ⋊ C22
HallC2×C13×D121 ⋊ C5
HallC13×C121 ⋊ C22×C5
HallC121⋊C5 ⋊ C22×C13
HallC2×D121 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D121⋊C5
commutator, cosocle, hypocenterC121C22×C5×C13
FrattiniC11C2×C13×AGL(1,𝔽11)
FittingC2×C13×C121C2×C5
socleC2×C11×C13AGL(1,𝔽11)
LCSG ▷ C121
UCSC1 ◁ C2×C13

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3146

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 17);