Finite Group Databasebeta

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C25×C3⋊(C3⋊(C7⋊D7)) #36347780

order22050
automorphism?
homologyAbelianization (H1) = C2×C25 · Schur multiplier (H2) = C3×C7

Aliases

direct productC25×C3⋊(C3⋊(C7⋊D7))
unambiguous semidirect productC3⋊(C25×C3⋊(C7⋊D7))
unambiguous semidirect productC7⋊(C25×C3⋊D21)

Splittings

Fitting, HallC32×C72×C25 ⋊ C2
derived, HallC32×C72 ⋊ C2×C25
HallC72×C25 ⋊ C3⋊D3
HallC32×C25 ⋊ C7⋊D7
SylowC72 ⋊ C3⋊D3×C25
SylowC32 ⋊ C25×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC25C3⋊(C3⋊(C7⋊D7))
commutator, hypocenterC32×C72C2×C25
FrattiniC5C5×C3⋊(C3⋊(C7⋊D7))
FittingC32×C72×C25C2
socle, cosocleC32×C5×C72C2×C5
prime radicalC5×C3⋊(C3⋊(C7⋊D7))C5
LCSG ▷ C32×C72
UCSC1 ◁ C25

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11025

Conjugacy classes & character table

5550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 217);