Finite Group Databasebeta

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C3×C49×C3⋊(C5⋊D5) #36347706

order22050
automorphism?
homologyAbelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C5

Aliases

direct productC3×C49×C3⋊(C5⋊D5)
unambiguous semidirect productC3⋊(C3×C49×C5⋊D5)
unambiguous semidirect productC5⋊(C3×D15×C49)

Splittings

Fitting, HallC32×C52×C49 ⋊ C2
derivedC3×C52 ⋊ C2×C3×C49
HallC52×C49 ⋊ C3×D3
HallC32×C49 ⋊ C5⋊D5
HallC32×C52 ⋊ C2×C49
SylowC52 ⋊ C3×D3×C49
SylowC32 ⋊ C49×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC3×C49C3⋊(C5⋊D5)
commutator, hypocenterC3×C52C2×C3×C49
FrattiniC7C3×C7×C3⋊(C5⋊D5)
FittingC32×C52×C49C2
socleC32×C52×C7C2×C7
prime radicalC3×C7×C3⋊(C5⋊D5)C7
cosocleC3×C52×C7C2×C3×C7
LCSG ▷ C3×C52
UCSC1 ◁ C3×C49

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7350

Conjugacy classes & character table

5733 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 143);