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C7⋊(C9⋊(D41⋊C5)) #38788922

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

Aliases

unambiguous semidirect productC7⋊(C9⋊(D41⋊C5))
unambiguous semidirect productC9⋊(C7⋊(D41⋊C5))
unambiguous semidirect product(C41⋊C5)⋊D63
unambiguous semidirect productD2583⋊C5

Splittings

Fitting, derived, HallC7×C9×C41 ⋊ C2×C5
HallC7×C9×C41⋊C5 ⋊ C2
HallD2583 ⋊ C5
HallC9×C41⋊C5 ⋊ D7
HallC7×C41⋊C5 ⋊ D9
HallC9×C41 ⋊ C5×D7
HallC7×C41 ⋊ C5×D9
HallC41⋊C5 ⋊ D63
HallC7×C9 ⋊ D41⋊C5
SylowC41 ⋊ C5×D63
SylowC9 ⋊ C7⋊(D41⋊C5)
SylowC7 ⋊ C9⋊(D41⋊C5)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC7×C9×C41C2×C5
FrattiniC3C3⋊(C7⋊(D41⋊C5))
socleC3×C7×C41C5×D3
LCSG ▷ C7×C9×C41
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 2583

A minimal faithful permutation representation — 2 generators on 57 points:

(2,6,7,23,27,3,4,12,14,22)(5,19,20,25,26,9,10,34,13,36)(8,31,32,33,21,16,17,41,18,11)(15,38,39,24,37,29,30,40,28,35)(43,44)(45,46)(47,48)(50,52)(51,55)(53,54)(56,57);(1,2,5,11,22,34,37,41,36,25,4,8,18,31,39,38,14,28,7,15,10,19,29,12,24,23,30,40,17,33,16,6,13,26,32,35,20,27,21,9,3)(42,43,45,47,48,46,44)(49,57,52,55,54,53,51,50,56)

Polycyclic presentation:

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

Conjugacy classes & character table

417 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 26);