Finite Group Databasebeta

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C5×C5⋊(D49⋊C9) #36347601

order22050
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C5⋊(D49⋊C9)
unambiguous semidirect productC5⋊(C5×D49⋊C9)
unambiguous semidirect product(C49⋊C9)⋊(C5×D5)
unambiguous semidirect productD245⋊(C5×C9)
unambiguous semidirect product(C5×D245)⋊C9

Splittings

derivedC5×C49 ⋊ C2×C5×C9
HallC52×C49⋊C9 ⋊ C2
HallC5×D245 ⋊ C9
HallC52×C49 ⋊ C2×C9
HallC49⋊C9 ⋊ C5×D5
SylowC49 ⋊ C5×C9×D5
SylowC52 ⋊ D49⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5C5⋊(D49⋊C3)
commutator, hypocenterC5×C49C2×C5×C9
FrattiniC3×C7C5×C5⋊AGL(1,𝔽7)
FittingC3×C52×C49C2×C3
socleC3×C52×C7AGL(1,𝔽7)
prime radicalC3×C5×D245C3
cosocleC3×C5×C49C2×C3×C5
LCSG ▷ C5×C49
UCSC1 ◁ C3×C5

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4410

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 38);