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(C31⋊C3)⋊((C5⋊D5)⋊C3) #28358456

order13950
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5

Aliases

unambiguous semidirect product(C31⋊C3)⋊((C5⋊D5)⋊C3)
unambiguous semidirect product(C5⋊(C5⋊(D31⋊C3)))⋊C3
unambiguous semidirect product#17987869⋊C3
unambiguous semidirect product#17987871⋊C3

Splittings

Fitting, socle, derived, HallC52×C31 ⋊ C2×C32
HallC52⋊C3×C31⋊C3 ⋊ C2
HallC5⋊D155 ⋊ C32
SylowC31 ⋊ C3×(C5⋊D5)⋊C3
SylowC52 ⋊ C3×D31⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C31C2×C32
LCSG ▷ C52×C31
UCSC1

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3^2,5^2,31|d^a=d^4,e^a=e^4,f^a=f^30,f^b=f^5,d^c=de,e^c=d^2e^3

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C5⋊D5)⋊C3×D31⋊C3, #3874⋊(D31⋊C3), C2×(C31⋊C3)⋊((C5⋊D5)⋊C3)
maximal normal subgroup of(C5⋊D5)⋊C3×D31⋊C3, #3874⋊(D31⋊C3), C2×(C31⋊C3)⋊((C5⋊D5)⋊C3)
maximal quotient of(C31⋊C3)⋊(#1039⋊C3), C2×(C31⋊C3)⋊((C5⋊D5)⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 99);