Finite Group Databasebeta

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C2×C5×D801 #30630827

order16020
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D801
unambiguous semidirect product(C2×C9)⋊(C5×D89)
unambiguous semidirect product(C2×C89)⋊(C5×D9)

Splittings

FittingC2×C5×C9×C89 ⋊ C2
derived, HallC9×C89 ⋊ C22×C5
HallC5×C9×C89 ⋊ C22
HallC5×C89 ⋊ C2×D9
SylowC89 ⋊ C2×C5×D9
HallC5×C9 ⋊ C2×D89
SylowC9 ⋊ C2×C5×D89

Subgroups

subgroupG/H
center, hypercenterC2×C5D801
commutator, cosocle, hypocenterC9×C89C22×C5
FrattiniC3C2×C5×D267
FittingC2×C5×C9×C89C2
socleC2×C3×C5×C89D3
LCSG ▷ C9×C89
UCSC1 ◁ C2×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8010

Conjugacy classes & character table

4020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16020, 32);