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C3⋊(C5⋊AGL(1,𝔽31)) #28358452

order13950
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C5⋊AGL(1,𝔽31))
unambiguous semidirect productC5⋊(C3⋊AGL(1,𝔽31))
unambiguous semidirect product((C31⋊C3)⋊C5)⋊D15
unambiguous semidirect product(C3⋊(C5⋊(D31⋊C3)))⋊C5
unambiguous semidirect product(C3⋊(C5⋊(D31⋊C5)))⋊C3

Splittings

Fitting, socle, derivedC3×C5×C31 ⋊ C2×C3×C5
HallC3×C5×(C31⋊C3)⋊C5 ⋊ C2
HallC5×ΓL(1,𝔽32) ⋊ C3×D3
HallC3×C31⋊C3 ⋊ C5×D5
SylowC31 ⋊ C3×C5×D15

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C31C2×C3×C5
LCSG ▷ C3×C5×C31
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,5,3,5,31|d^a=d^2,e^a=e^4,f^a=f^30,f^b=f^5,f^c=f^16

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD15×AGL(1,𝔽31), D5×C3⋊AGL(1,𝔽31), D3×C5⋊AGL(1,𝔽31), …
maximal normal subgroup ofD15×AGL(1,𝔽31), D5×C3⋊AGL(1,𝔽31), D3×C5⋊AGL(1,𝔽31), …
maximal quotient ofC3⋊(((C31⋊C3)⋊C5)⋊Dic5), C2×C3⋊(C5⋊AGL(1,𝔽31))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 95);