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C2×C9×D995 #49089083

order35820
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D995
unambiguous semidirect product(C2×C5)⋊(C9×D199)

Splittings

FittingC2×C5×C9×C199 ⋊ C2
derived, HallC5×C199 ⋊ C22×C9
HallC5×C9×C199 ⋊ C22
HallC9×C199 ⋊ C2×D5
SylowC199 ⋊ C2×C9×D5
HallC5×C9 ⋊ C2×D199
SylowC5 ⋊ C2×C9×D199

Subgroups

subgroupG/H
center, hypercenterC2×C9D995
commutator, hypocenterC5×C199C22×C9
FrattiniC3C2×C3×D995
FittingC2×C5×C9×C199C2
socleC2×C3×C5×C199C2×C3
prime radicalC2×C3×D995C3
cosocleC3×C5×C199C22×C3
LCSG ▷ C5×C199
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17910

Conjugacy classes & character table

8982 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35820, 38);