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C5⋊(C5⋊#10587717) #28331600

order13650
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

unambiguous semidirect productC5⋊(C5⋊#10587717)

Splittings

Fitting, socle, derived, HallC52×C7×C13 ⋊ C2×C3
HallC52×#63271 ⋊ C2
HallC7×C5⋊D65 ⋊ C3
HallC5⋊D65 ⋊ ΓL(1,𝔽8)
HallC52×C13 ⋊ C2×ΓL(1,𝔽8)
Hall#63271 ⋊ C5⋊D5
HallC52×C7 ⋊ D13⋊C3
HallC7×C13 ⋊ C3×C5⋊D5
SylowC52 ⋊ #10587717
SylowC13 ⋊ ΓL(1,𝔽8)×C5⋊D5
SylowC7 ⋊ C5⋊(C5⋊(D13⋊C3))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7×C13C2×C3
LCSG ▷ C52×C7×C13
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2275

Polycyclic presentation:

2,3,5^2,7,13|c^a=c^4,d^a=d^4,f^a=f^12,e^b=e^2,f^b=f^9

Conjugacy classes & character table

420 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#41031708, D5×C5⋊#10587717, #10587721⋊(C5⋊D5), …
maximal normal subgroup of#41031708, D5×C5⋊#10587717, #10587721⋊(C5⋊D5), …
maximal quotient of#41031386, C2×C5⋊(C5⋊#10587717)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13650, 88);