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D15⋊(D71⋊C7) #44447181

order29820
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD15⋊(D71⋊C7)
unambiguous semidirect product(C3⋊(D71⋊C7))⋊D5
unambiguous semidirect product(D15⋊D71)⋊C7
unambiguous semidirect product(C5⋊(D71⋊C7))⋊D3

Splittings

Fitting, socle, derived, HallC3×C5×C71 ⋊ C22×C7
HallC3×C5×C71⋊C7 ⋊ C22
HallD15⋊D71 ⋊ C7
HallC5×C71⋊C7 ⋊ C2×D3
HallC3×C71⋊C7 ⋊ C2×D5
HallC71⋊C7 ⋊ D3×D5
HallC5×C71 ⋊ C2×D3×C7
HallC3×C71 ⋊ C2×C7×D5
SylowC71 ⋊ D3×C7×D5
HallC3×C5 ⋊ C2×D71⋊C7
SylowC5 ⋊ D3×D71⋊C7
SylowC3 ⋊ D5×D71⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C71C22×C7
LCSG ▷ C3×C5×C71
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1065

Polycyclic presentation:

2^2,7,3,5,71|e^a=e^4,f^a=f^70,d^b=d^2,e^b=e^4,f^c=f^45

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 69);