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(C7⋊C9)⋊(D41⋊C5) #38788932

order25830
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C7⋊C9)⋊(D41⋊C5)
unambiguous semidirect product(C41⋊C5)⋊(D7⋊C9)
unambiguous semidirect product(C7⋊(D41⋊C5))⋊C9
unambiguous semidirect product(C41⋊(D7⋊C9))⋊C5

Splittings

derived, HallC7×C41 ⋊ C2×C5×C9
HallC7⋊C9×C41⋊C5 ⋊ C2
HallC41⋊(D7⋊C9) ⋊ C5
HallC7⋊(D41⋊C5) ⋊ C9
HallC41×C7⋊C9 ⋊ C2×C5
HallC7×C41⋊C5 ⋊ C2×C9
HallD287 ⋊ C5×C9
HallC41⋊C5 ⋊ D7⋊C9
HallC7⋊C9 ⋊ D41⋊C5
SylowC41 ⋊ C5×D7⋊C9
SylowC7 ⋊ C9×D41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC3ΓL(1,𝔽8)⋊(D41⋊C5)
commutator, hypocenterC7×C41C2×C5×C9
Fitting, socle, cosocleC3×C7×C41C2×C3×C5
prime radicalC3×C7⋊(D41⋊C5)C3
LCSG ▷ C7×C41
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2583

Polycyclic presentation:

2,3,5,7,41,3|b^3=f,d^a=d^6,e^a=e^40,d^b=d^2,e^c=e^10

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 36);