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C3×C3⋊(C5⋊(C5⋊(C7⋊D7))) #36348076

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

Aliases

direct productC3×C3⋊(C5⋊(C5⋊(C7⋊D7)))
unambiguous semidirect productC3⋊(C3×C5⋊(C5⋊(C7⋊D7)))
unambiguous semidirect productC5⋊(C3×C3⋊(C5⋊(C7⋊D7)))

Splittings

Fitting, socle, HallC32×C52×C72 ⋊ C2
derivedC3×C52×C72 ⋊ C2×C3
HallC52×C72 ⋊ C3×D3
HallC32×C72 ⋊ C5⋊D5
HallC32×C52 ⋊ C7⋊D7
SylowC72 ⋊ C3×C3⋊(C5⋊D5)
SylowC52 ⋊ C3×C3⋊(C7⋊D7)
SylowC32 ⋊ C5⋊(C5⋊(C7⋊D7))

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C5⋊(C5⋊(C7⋊D7)))
commutator, cosocle, hypocenterC3×C52×C72C2×C3
FrattiniC1G
Fitting, socleC32×C52×C72C2
LCSG ▷ C3×C52×C72
UCSC1 ◁ C3

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7350

Conjugacy classes & character table

5517 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 513);