Finite Group Databasebeta

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C5×C17×D43⋊C3 #36346705

order21930
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×D43⋊C3
unambiguous semidirect productD43⋊(C3×C5×C17)
unambiguous semidirect product(C43⋊C3)⋊(C2×C5×C17)
unambiguous semidirect product(C5×D43)⋊(C3×C17)
unambiguous semidirect product(C17×D43)⋊(C3×C5)
unambiguous semidirect product(C5×C17×D43)⋊C3

Splittings

Fitting, socle, HallC5×C17×C43 ⋊ C2×C3
derived, SylowC43 ⋊ C2×C3×C5×C17
HallC5×C17×C43⋊C3 ⋊ C2
HallC5×C17×D43 ⋊ C3
HallC17×C43⋊C3 ⋊ C2×C5
HallC17×D43 ⋊ C3×C5
HallC17×C43 ⋊ C2×C3×C5
HallC5×C43⋊C3 ⋊ C2×C17
HallC5×D43 ⋊ C3×C17
HallC5×C43 ⋊ C2×C3×C17
HallC43⋊C3 ⋊ C2×C5×C17
HallD43 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC5×C17D43⋊C3
commutator, cosocle, hypocenterC43C2×C3×C5×C17
FrattiniC1G
Fitting, socleC5×C17×C43C2×C3
LCSG ▷ C43
UCSC1 ◁ C5×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3655

Conjugacy classes & character table

1105 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21930, 18);