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C2×C9×D895 #44567339

order32220
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D895
unambiguous semidirect product(C2×C5)⋊(C9×D179)
unambiguous semidirect product(C2×C179)⋊(C9×D5)

Splittings

FittingC2×C5×C9×C179 ⋊ C2
derived, HallC5×C179 ⋊ C22×C9
HallC5×C9×C179 ⋊ C22
HallC9×C179 ⋊ C2×D5
SylowC179 ⋊ C2×C9×D5
HallC5×C9 ⋊ C2×D179
SylowC5 ⋊ C2×C9×D179

Subgroups

subgroupG/H
center, hypercenterC2×C9D895
commutator, hypocenterC5×C179C22×C9
FrattiniC3C2×C3×D895
FittingC2×C5×C9×C179C2
socleC2×C3×C5×C179C2×C3
prime radicalC2×C3×D895C3
cosocleC3×C5×C179C22×C3
LCSG ▷ C5×C179
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16110

Conjugacy classes & character table

8082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32220, 26);