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C3⋊(D31⋊C5) #11745382

order930
isoclinismisoclinic class of C3⋊(D31⋊C5)
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(D31⋊C5)
unambiguous semidirect productΓL(1,𝔽32)⋊D3
unambiguous semidirect productD93⋊C5

Splittings

Fitting, socle, derived, HallC3×C31 ⋊ C2×C5
HallC3×ΓL(1,𝔽32) ⋊ C2
HallD93 ⋊ C5
HallΓL(1,𝔽32) ⋊ D3
SylowC31 ⋊ C5×D3
SylowC3 ⋊ D31⋊C5

Subgroups

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

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 93

Polycyclic presentation:

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

Conjugacy classes & character table

24 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D31⋊C5, C2×C3⋊(D31⋊C5), C9⋊(D31⋊C5), …
maximal normal subgroup ofD3×D31⋊C5, C2×C3⋊(D31⋊C5), C3⋊AGL(1,𝔽31), …
maximal quotient ofC3⋊(Dic31⋊C5), C2×C3⋊(D31⋊C5), C9⋊(D31⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(930, 5);