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C2×C17×C5⋊(D37⋊C3) #49179809

order37740
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×C5⋊(D37⋊C3)
unambiguous semidirect product(C2×C5)⋊(C17×D37⋊C3)
unambiguous semidirect product(C2×C37⋊C3)⋊(D5×C17)
unambiguous semidirect product(C2×D185)⋊(C3×C17)
unambiguous semidirect product(C2×C17×D185)⋊C3

Splittings

Fitting, socleC2×C5×C17×C37 ⋊ C2×C3
derived, HallC5×C37 ⋊ C22×C3×C17
HallC2×C17×D185 ⋊ C3
HallC5×C17×C37⋊C3 ⋊ C22
HallC5×C17×C37 ⋊ C22×C3
HallC17×C37⋊C3 ⋊ C2×D5
HallC2×D185 ⋊ C3×C17
HallC17×C37 ⋊ C2×C3×D5
HallC5×C37⋊C3 ⋊ C22×C17
HallC37⋊C3 ⋊ C2×D5×C17
HallC5×C17 ⋊ C2×D37⋊C3
SylowC37 ⋊ C2×C3×D5×C17
SylowC5 ⋊ C2×C17×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C17C5⋊(D37⋊C3)
commutator, cosocle, hypocenterC5×C37C22×C3×C17
FrattiniC1G
Fitting, socleC2×C5×C17×C37C2×C3
LCSG ▷ C5×C37
UCSC1 ◁ C2×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6290

Conjugacy classes & character table

1428 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37740, 64);