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C32×C491⋊C5 #36348343

order22095
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C491⋊C5
unambiguous semidirect productC491⋊(C32×C5)
unambiguous semidirect product(C3×C491)⋊(C3×C5)
unambiguous semidirect product(C32×C491)⋊C5

Splittings

Fitting, socle, HallC32×C491 ⋊ C5
derived, SylowC491 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC32C491⋊C5
commutator, cosocle, hypocenterC491C32×C5
FrattiniC1G
Fitting, socleC32×C491C5
LCSG ▷ C491
UCSC1 ◁ C32

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4419

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22095, 4);