Finite Group Databasebeta

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C2×C9×D565 #35204792

order20340
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D565
unambiguous semidirect product(C2×C5)⋊(C9×D113)
unambiguous semidirect product(C2×C113)⋊(C9×D5)

Splittings

FittingC2×C5×C9×C113 ⋊ C2
derived, HallC5×C113 ⋊ C22×C9
HallC5×C9×C113 ⋊ C22
HallC9×C113 ⋊ C2×D5
SylowC113 ⋊ C2×C9×D5
HallC5×C9 ⋊ C2×D113
SylowC5 ⋊ C2×C9×D113

Subgroups

subgroupG/H
center, hypercenterC2×C9D565
commutator, hypocenterC5×C113C22×C9
FrattiniC3C2×C3×D565
FittingC2×C5×C9×C113C2
socleC2×C3×C5×C113C2×C3
prime radicalC2×C3×D565C3
cosocleC3×C5×C113C22×C3
LCSG ▷ C5×C113
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10170

Conjugacy classes & character table

5112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20340, 34);