Finite Group Databasebeta

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C5×C17⋊(D43⋊C3) #36346707

order21930
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17⋊(D43⋊C3)
unambiguous semidirect productC17⋊(C5×D43⋊C3)
unambiguous semidirect product(C43⋊C3)⋊(C5×D17)
unambiguous semidirect productD731⋊(C3×C5)
unambiguous semidirect product(C5×D731)⋊C3

Splittings

Fitting, socle, HallC5×C17×C43 ⋊ C2×C3
derived, HallC17×C43 ⋊ C2×C3×C5
HallC5×C17×C43⋊C3 ⋊ C2
HallC5×D731 ⋊ C3
HallC17×C43⋊C3 ⋊ C2×C5
HallD731 ⋊ C3×C5
HallC5×C43⋊C3 ⋊ D17
HallC5×C43 ⋊ C3×D17
HallC43⋊C3 ⋊ C5×D17
HallC5×C17 ⋊ D43⋊C3
SylowC43 ⋊ C3×C5×D17
SylowC17 ⋊ C5×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C17⋊(D43⋊C3)
commutator, cosocle, hypocenterC17×C43C2×C3×C5
FrattiniC1G
Fitting, socleC5×C17×C43C2×C3
LCSG ▷ C17×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3655

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21930, 20);