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C4×C41×C41⋊C5 #46777398

order33620
automorphism?
homologyAbelianization (H1) = C4×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productC4×C41×C41⋊C5
unambiguous semidirect product(C4×C41)⋊(C5×C41)

Splittings

Fitting, HallC4×C412 ⋊ C5
derivedC41 ⋊ C4×C5×C41
SylowC412 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC4×C41C41⋊C5
commutator, hypocenterC41C4×C5×C41
FrattiniC2C2×C41×C41⋊C5
FittingC4×C412C5
socleC2×C412C2×C5
prime radicalC2×C41×C41⋊C5C2
cosocleC2×C41C2×C5×C41
LCSG ▷ C41
UCSC1 ◁ C4×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 820

Conjugacy classes & character table

2132 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33620, 33);