Finite Group Databasebeta

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C49×C3⋊(C3⋊(C5⋊D5)) #36347712

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

Aliases

direct productC49×C3⋊(C3⋊(C5⋊D5))
unambiguous semidirect productC3⋊(C49×C3⋊(C5⋊D5))
unambiguous semidirect productC5⋊(C49×C3⋊D15)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC49C3⋊(C3⋊(C5⋊D5))
commutator, hypocenterC32×C52C2×C49
FrattiniC7C7×C3⋊(C3⋊(C5⋊D5))
FittingC32×C52×C49C2
socle, cosocleC32×C52×C7C2×C7
prime radicalC7×C3⋊(C3⋊(C5⋊D5))C7
LCSG ▷ C32×C52
UCSC1 ◁ C49

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11025

Conjugacy classes & character table

5586 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 149);