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(C5⋊D5)⋊#10625202 #49150256

order37050
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

unambiguous semidirect product(C5⋊D5)⋊#10625202

Splittings

Fitting, socle, derived, HallC52×C13×C19 ⋊ C2×C3
HallC52⋊#10625202 ⋊ C2
HallC13×C19×C5⋊D5 ⋊ C3
HallC19×C5⋊D5 ⋊ C13⋊C3
HallC13×C5⋊D5 ⋊ C19⋊C3
HallC52×C19 ⋊ C2×C13⋊C3
HallC52×C13 ⋊ C2×C19⋊C3
HallC13×C19 ⋊ (C5⋊D5)⋊C3
HallC5⋊D5 ⋊ #10625202
SylowC52 ⋊ C2×#10625202
SylowC19 ⋊ (C5⋊D5)⋊(C13⋊C3)
SylowC13 ⋊ (C5⋊D5)⋊(C19⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C13×C19C2×C3
LCSG ▷ C52×C13×C19
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3705

Polycyclic presentation:

2,3,5^2,13,19|c^a=c^4,d^a=d^4,c^b=cd^3,d^b=c^4d^3,e^b=e^3,f^b=f^7

Conjugacy classes & character table

1158 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 82);