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D13⋊C3×D187 #44415748

order29172
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD13⋊C3×D187
unambiguous semidirect productD13⋊(C3×D187)
unambiguous semidirect product(C11×D13⋊C3)⋊D17
unambiguous semidirect product(C17×D13⋊C3)⋊D11
unambiguous semidirect product(D13×D187)⋊C3

Splittings

Fitting, socle, derived, HallC11×C13×C17 ⋊ C22×C3
HallD13×D187 ⋊ C3
HallC11×C17×C13⋊C3 ⋊ C22
HallC17×C13⋊C3 ⋊ C2×D11
HallC11×C13⋊C3 ⋊ C2×D17
HallC13×C17 ⋊ C2×C3×D11
HallC11×C17 ⋊ C2×D13⋊C3
HallC11×C13 ⋊ C2×C3×D17
HallC13⋊C3 ⋊ C2×D187
SylowC17 ⋊ D11×D13⋊C3
SylowC13 ⋊ C2×C3×D187
SylowC11 ⋊ D17×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C13×C17C22×C3
LCSG ▷ C11×C13×C17
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2431

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 40);