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D5×(C13⋊C3)⋊D41 #44544373

order31980
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD5×(C13⋊C3)⋊D41
unambiguous semidirect product(D5×C13⋊C3)⋊D41
unambiguous semidirect product(D5×C41)⋊(D13⋊C3)
unambiguous semidirect product(D5×D533)⋊C3

Splittings

Fitting, socle, derived, HallC5×C13×C41 ⋊ C22×C3
HallD5×D533 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C22
HallC13⋊C3×C41 ⋊ C2×D5
HallC13×C41 ⋊ C2×C3×D5
HallC5×C41 ⋊ C2×D13⋊C3
HallC5×C13⋊C3 ⋊ C2×D41
HallC5×C13 ⋊ C2×C3×D41
SylowC41 ⋊ D5×D13⋊C3
HallC13⋊C3 ⋊ D5×D41
SylowC13 ⋊ C3×D5×D41
SylowC5 ⋊ C2×(C13⋊C3)⋊D41

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13×C41C22×C3
LCSG ▷ C5×C13×C41
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 101);