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D13⋊C3×D203 #44539877

order31668
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD13⋊C3×D203
unambiguous semidirect productD13⋊(C3×D203)
unambiguous semidirect product(C7×D13⋊C3)⋊D29
unambiguous semidirect product(C29×D13⋊C3)⋊D7

Splittings

Fitting, socle, derived, HallC7×C13×C29 ⋊ C22×C3
HallD13×D203 ⋊ C3
HallC7×C29×C13⋊C3 ⋊ C22
HallC29×C13⋊C3 ⋊ C2×D7
HallC13×C29 ⋊ C2×C3×D7
HallC7×C13⋊C3 ⋊ C2×D29
HallC7×C29 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C2×C3×D29
HallC13⋊C3 ⋊ C2×D203
SylowC29 ⋊ D7×D13⋊C3
SylowC13 ⋊ C2×C3×D203
SylowC7 ⋊ D29×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C29C22×C3
LCSG ▷ C7×C13×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2639

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 172);