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C5⋊(D31⋊C5) #13095463

order1550
isoclinismisoclinic class of C5⋊(D31⋊C5)
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC5⋊(D31⋊C5)
unambiguous semidirect productΓL(1,𝔽32)⋊D5
unambiguous semidirect productD155⋊C5

Splittings

Fitting, socle, derivedC5×C31 ⋊ C2×C5
HallC5×ΓL(1,𝔽32) ⋊ C2
SylowC31 ⋊ C5×D5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C31C2×C5
LCSG ▷ C5×C31
UCSC1

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 155

Polycyclic presentation:

2,5^2,31|c^a=c^4,d^a=d^30,d^b=d^4

Conjugacy classes & character table

35 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×D31⋊C5, C2×C5⋊(D31⋊C5), C5⋊AGL(1,𝔽31), …
maximal normal subgroup ofD5×D31⋊C5, C2×C5⋊(D31⋊C5), C5⋊AGL(1,𝔽31), …
maximal quotient ofΓL(1,𝔽32)⋊Dic5, C2×C5⋊(D31⋊C5), C3×C5⋊(D31⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1550, 9);