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C5×C9⋊#63121 #26043433

order11700
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9⋊#63121
unambiguous semidirect productC9⋊(C5×#63121)

Splittings

Fitting, HallC52×C9×C13 ⋊ C4
derivedC5×C9×C13 ⋊ C4×C5
HallC52×C13 ⋊ Dic9
HallC52×C9 ⋊ #261
HallC9×C13 ⋊ C5×AGL(1,𝔽5)
SylowC52 ⋊ C9⋊#261
SylowC13 ⋊ C5×C9⋊AGL(1,𝔽5)
SylowC9 ⋊ C5×#63121

Subgroups

subgroupG/H
center, hypercenterC5C9⋊#63121
commutator, hypocenterC5×C9×C13C4×C5
FrattiniC3C5×C3⋊#63121
FittingC52×C9×C13C4
socleC3×C52×C13Dic3
prime radicalC3×C5×D65D3
cosocleC9×D65C2×C5
LCSG ▷ C5×C9×C13
UCSC1 ◁ C5

78 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 280);