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C13×D17×D13⋊C3 #46828217

order34476
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×D17×D13⋊C3
unambiguous semidirect productD13⋊(C3×C13×D17)
unambiguous semidirect product(D13×D17)⋊(C3×C13)
unambiguous semidirect product(D17×C13⋊C3)⋊(C2×C13)
unambiguous semidirect product(C17×D13⋊C3)⋊(C2×C13)
unambiguous semidirect product(C17⋊(D13⋊C3))⋊(C2×C13)

Splittings

Fitting, socle, HallC132×C17 ⋊ C22×C3
derivedC13×C17 ⋊ C22×C3×C13
HallC13×D13×D17 ⋊ C3
HallC13×C17×C13⋊C3 ⋊ C22
HallC13×C13⋊C3 ⋊ C2×D17
SylowC132 ⋊ C2×C3×D17
SylowC17 ⋊ C2×C13×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC13D17×D13⋊C3
commutator, cosocle, hypocenterC13×C17C22×C3×C13
FrattiniC1G
Fitting, socleC132×C17C22×C3
LCSG ▷ C13×C17
UCSC1 ◁ C13

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1326

Conjugacy classes & character table

1040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34476, 98);