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C2×D5×C1681 #46777384

order33620
automorphism?
homologyAbelianization (H1) = C22×C1681 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C1681
unambiguous semidirect productC5⋊(C22×C1681)
unambiguous semidirect product(C2×C5)⋊(C2×C1681)

Splittings

FittingC2×C5×C1681 ⋊ C2
derived, SylowC5 ⋊ C22×C1681
HallC5×C1681 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C1681D5
commutator, hypocenterC5C22×C1681
FrattiniC41C2×D5×C41
FittingC2×C5×C1681C2
socleC2×C5×C41C2×C41
prime radicalC2×D5×C41C41
cosocleC5×C41C22×C41
LCSG ▷ C5
UCSC1 ◁ C2×C1681

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16810

Conjugacy classes & character table

13448 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33620, 19);