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C3×(C281⋊C5)⋊C7 #44443161

order29505
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C281⋊C5)⋊C7
unambiguous semidirect product(C281⋊C5)⋊(C3×C7)
unambiguous semidirect product(C281⋊C7)⋊(C3×C5)
unambiguous semidirect product(C3×C281⋊C5)⋊C7
unambiguous semidirect product(C3×C281⋊C7)⋊C5

Splittings

Fitting, socle, HallC3×C281 ⋊ C5×C7
derived, SylowC281 ⋊ C3×C5×C7
HallC3×C281⋊C7 ⋊ C5
HallC3×C281⋊C5 ⋊ C7
HallC281⋊C7 ⋊ C3×C5
HallC281⋊C5 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC3(C281⋊C5)⋊C7
commutator, cosocle, hypocenterC281C3×C5×C7
FrattiniC1G
Fitting, socleC3×C281C5×C7
LCSG ▷ C281
UCSC1 ◁ C3

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 843

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29505, 4);