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C31×(C31⋊C3)⋊C5 #28385707

order14415
isoclinismisoclinic class of (C31⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C3×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×(C31⋊C3)⋊C5
unambiguous semidirect product(C31⋊C3)⋊(C5×C31)
unambiguous semidirect productΓL(1,𝔽32)⋊(C3×C31)

Splittings

Fitting, socle, SylowC312 ⋊ C3×C5
derivedC31 ⋊ C3×C5×C31
HallC31×ΓL(1,𝔽32) ⋊ C3
HallC31×C31⋊C3 ⋊ C5

Subgroups

subgroupG/H
center, hypercenterC31(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C3×C5×C31
FrattiniC1G
Fitting, socleC312C3×C5
LCSG ▷ C31
UCSC1 ◁ C31

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 465

Conjugacy classes & character table

527 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC31×AGL(1,𝔽31), ((C31⋊C3)⋊C5)⋊D31, D31×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC31×AGL(1,𝔽31), ((C31⋊C3)⋊C5)⋊D31, D31×(C31⋊C3)⋊C5, …
maximal quotient ofC2×C31×(C31⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14415, 6);