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C3⋊(C7⋊(D31⋊C25)) #45654396

order32550
automorphism?
homologyAbelianization (H1) = C2×C25 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C7⋊(D31⋊C25))
unambiguous semidirect productC7⋊(C3⋊(D31⋊C25))
unambiguous semidirect product(C31⋊C25)⋊D21
unambiguous semidirect productD651⋊C25

Splittings

derived, HallC3×C7×C31 ⋊ C2×C25
HallC3×C7×C31⋊C25 ⋊ C2
HallC7×C31⋊C25 ⋊ D3
HallC3×C31⋊C25 ⋊ D7
HallD651 ⋊ C25
HallC31⋊C25 ⋊ D21
HallC7×C31 ⋊ D3×C25
HallC3×C31 ⋊ D7×C25
SylowC31 ⋊ C25×D21
HallC3×C7 ⋊ D31⋊C25
SylowC7 ⋊ C3⋊(D31⋊C25)
SylowC3 ⋊ C7⋊(D31⋊C25)

Subgroups

subgroupG/H
center, Frattini, hypercenterC5C3⋊(C7⋊(D31⋊C5))
commutator, hypocenterC3×C7×C31C2×C25
Fitting, socle, cosocleC3×C5×C7×C31C2×C5
prime radicalC5×D651C5
LCSG ▷ C3×C7×C31
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16275

Polycyclic presentation:

2,3,5,7,31,5|c^5=f,b^a=b^2,d^a=d^6,e^a=e^30,e^c=e^16

Conjugacy classes & character table

615 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 32);