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C2×C9×D455 #30655178

order16380
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D455
unambiguous semidirect product(C2×C5)⋊(C9×D91)

Splittings

FittingC2×C5×C7×C9×C13 ⋊ C2
derived, HallC5×C7×C13 ⋊ C22×C9
HallC5×C7×C9×C13 ⋊ C22
HallC7×C9×C13 ⋊ C2×D5
HallC5×C9×C13 ⋊ C2×D7
HallC5×C7×C9 ⋊ C2×D13
HallC9×C13 ⋊ C2×D35
HallC7×C13 ⋊ C2×C9×D5
HallC5×C13 ⋊ C2×C9×D7
HallC7×C9 ⋊ C2×D65
HallC5×C9 ⋊ C2×D91
HallC5×C7 ⋊ C2×C9×D13
SylowC13 ⋊ C2×C9×D35
SylowC7 ⋊ C2×C9×D65
SylowC5 ⋊ C2×C9×D91

Subgroups

subgroupG/H
center, hypercenterC2×C9D455
commutator, hypocenterC5×C7×C13C22×C9
FrattiniC3C2×C3×D455
FittingC2×C5×C7×C9×C13C2
socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×D455C3
cosocleC3×C5×C7×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C9

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8190

Conjugacy classes & character table

4122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 228);