Finite Group Databasebeta

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C2×C41×D41⋊C5 #46777435

order33620
automorphism?
homologyAbelianization (H1) = C22×C5×C41 · Schur multiplier (H2) = C2

Aliases

direct productC2×C41×D41⋊C5
unambiguous semidirect productD41⋊(C2×C5×C41)
unambiguous semidirect product(C2×D41)⋊(C5×C41)
unambiguous semidirect product(C41⋊C5)⋊(C22×C41)
unambiguous semidirect product(C2×C41⋊C5)⋊(C2×C41)

Splittings

Fitting, socleC2×C412 ⋊ C2×C5
derivedC41 ⋊ C22×C5×C41
HallC41×C41⋊C5 ⋊ C22
HallC2×C41×D41 ⋊ C5
SylowC412 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC2×C41D41⋊C5
commutator, cosocle, hypocenterC41C22×C5×C41
FrattiniC1G
Fitting, socleC2×C412C2×C5
LCSG ▷ C41
UCSC1 ◁ C2×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 820

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33620, 70);