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C5×C3⋊(C3⋊(C5⋊(C7⋊D7))) #36348082

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

Aliases

direct productC5×C3⋊(C3⋊(C5⋊(C7⋊D7)))
unambiguous semidirect productC3⋊(C5×C3⋊(C5⋊(C7⋊D7)))
unambiguous semidirect productC5⋊(C5×C3⋊(C3⋊(C7⋊D7)))
unambiguous semidirect productC7⋊(C5×C3⋊D105)

Splittings

Fitting, socle, HallC32×C52×C72 ⋊ C2
derivedC32×C5×C72 ⋊ C2×C5
HallC52×C72 ⋊ C3⋊D3
HallC32×C72 ⋊ C5×D5
HallC32×C52 ⋊ C7⋊D7
SylowC72 ⋊ C5×C3⋊D15
SylowC52 ⋊ C3⋊(C3⋊(C7⋊D7))
SylowC32 ⋊ C5×C5⋊(C7⋊D7)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C3⋊(C5⋊(C7⋊D7)))
commutator, cosocle, hypocenterC32×C5×C72C2×C5
FrattiniC1G
Fitting, socleC32×C52×C72C2
LCSG ▷ C32×C5×C72
UCSC1 ◁ C5

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4410

Conjugacy classes & character table

5520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 519);