Finite Group Databasebeta

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C7×C3⋊(C3⋊(C5⋊D35)) #36348084

order22050
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C3×C5

Aliases

direct productC7×C3⋊(C3⋊(C5⋊D35))
unambiguous semidirect productC3⋊(C7×C3⋊(C5⋊D35))
unambiguous semidirect productC5⋊(C7×C3⋊D105)
unambiguous semidirect productC7⋊(C7×C3⋊(C3⋊(C5⋊D5)))

Splittings

Fitting, socle, HallC32×C52×C72 ⋊ C2
derivedC32×C52×C7 ⋊ C2×C7
HallC52×C72 ⋊ C3⋊D3
HallC32×C72 ⋊ C5⋊D5
HallC32×C52 ⋊ C7×D7
SylowC72 ⋊ C3⋊(C3⋊(C5⋊D5))
SylowC52 ⋊ C7×C3⋊D21
SylowC32 ⋊ C7×C5⋊D35

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C3⋊(C5⋊D35))
commutator, cosocle, hypocenterC32×C52×C7C2×C7
FrattiniC1G
Fitting, socleC32×C52×C72C2
LCSG ▷ C32×C52×C7
UCSC1 ◁ C7

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3150

Conjugacy classes & character table

5523 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 521);