Finite Group Databasebeta

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D17×C5⋊(D37⋊C3) #49179802

order37740
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD17×C5⋊(D37⋊C3)
unambiguous semidirect product(C5×D17)⋊(D37⋊C3)
unambiguous semidirect product(D17×C37⋊C3)⋊D5
unambiguous semidirect product(D17×D185)⋊C3

Splittings

Fitting, socle, derived, HallC5×C17×C37 ⋊ C22×C3
HallD17×D185 ⋊ C3
HallC5×C17×C37⋊C3 ⋊ C22
HallC17×C37⋊C3 ⋊ C2×D5
HallC17×C37 ⋊ C2×C3×D5
HallC5×C37⋊C3 ⋊ C2×D17
HallC5×C37 ⋊ C2×C3×D17
HallC37⋊C3 ⋊ D5×D17
HallC5×C17 ⋊ C2×D37⋊C3
SylowC37 ⋊ C3×D5×D17
SylowC17 ⋊ C2×C5⋊(D37⋊C3)
SylowC5 ⋊ D17×D37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C17×C37C22×C3
LCSG ▷ C5×C17×C37
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3145

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37740, 57);