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C49×(C5⋊D5)⋊C9 #36347606

order22050
automorphism?
homologyAbelianization (H1) = C2×C9×C49 · Schur multiplier (H2) = C5

Aliases

direct productC49×(C5⋊D5)⋊C9
unambiguous semidirect product(C5⋊D5)⋊(C9×C49)

Splittings

derived, SylowC52 ⋊ C2×C9×C49
HallC49×C52⋊C9 ⋊ C2
HallC49×C5⋊D5 ⋊ C9
HallC52×C49 ⋊ C2×C9
HallC52⋊C9 ⋊ C2×C49
HallC5⋊D5 ⋊ C9×C49

Subgroups

subgroupG/H
center, hypercenterC3×C49(C5⋊D5)⋊C3
commutator, hypocenterC52C2×C9×C49
FrattiniC3×C7C7×(C5⋊D5)⋊C3
FittingC3×C52×C49C2×C3
socle, cosocleC3×C52×C7C2×C3×C7
prime radicalC3×C7×C5⋊D5C3×C7
LCSG ▷ C52
UCSC1 ◁ C3×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2205

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 43);