Finite Group Databasebeta

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C17×C5⋊(D43⋊C3) #36346709

order21930
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C5⋊(D43⋊C3)
unambiguous semidirect productC5⋊(C17×D43⋊C3)
unambiguous semidirect product(C43⋊C3)⋊(D5×C17)
unambiguous semidirect productD215⋊(C3×C17)
unambiguous semidirect product(C17×D215)⋊C3

Splittings

Fitting, socle, HallC5×C17×C43 ⋊ C2×C3
derived, HallC5×C43 ⋊ C2×C3×C17
HallC5×C17×C43⋊C3 ⋊ C2
HallC17×D215 ⋊ C3
HallC17×C43⋊C3 ⋊ D5
HallC17×C43 ⋊ C3×D5
HallC5×C43⋊C3 ⋊ C2×C17
HallD215 ⋊ C3×C17
HallC43⋊C3 ⋊ D5×C17
HallC5×C17 ⋊ D43⋊C3
SylowC43 ⋊ C3×D5×C17
SylowC5 ⋊ C17×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC17C5⋊(D43⋊C3)
commutator, cosocle, hypocenterC5×C43C2×C3×C17
FrattiniC1G
Fitting, socleC5×C17×C43C2×C3
LCSG ▷ C5×C43
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3655

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21930, 22);