Finite Group Databasebeta

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C2×D8405 #46777385

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

Aliases

dihedralD16810
direct productC2×D8405
unambiguous semidirect product(C2×C5)⋊D1681
unambiguous semidirect product(C2×C1681)⋊D5

Splittings

FittingC2×C5×C1681 ⋊ C2
derived, HallC5×C1681 ⋊ C22
SylowC1681 ⋊ C2×D5
SylowC5 ⋊ C2×D1681

Subgroups

subgroupG/H
center, hypercenterC2D8405
commutator, cosocle, hypocenterC5×C1681C22
FrattiniC41C2×D205
FittingC2×C5×C1681C2
socleC2×C5×C41D41
LCSG ▷ C5×C1681
UCSC1 ◁ C2

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 1688
transitive degreeμt(G) = 16810

A minimal faithful permutation representation — 2 generators on 1688 points:

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Conjugacy classes & character table

8408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33620, 20);