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C2×C3×C5⋊AGL(1,𝔽31) #42124692

order27900
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C5⋊AGL(1,𝔽31)
unambiguous semidirect product(C2×C5)⋊(C3×AGL(1,𝔽31))
unambiguous semidirect product(C2×(C31⋊C3)⋊C5)⋊(C3×D5)
unambiguous semidirect product(C2×C5⋊(D31⋊C3))⋊(C3×C5)
unambiguous semidirect product(C2×C5⋊(D31⋊C5))⋊C32
unambiguous semidirect product(C2×C3×C5⋊(D31⋊C3))⋊C5
unambiguous semidirect product(C2×C3×C5⋊(D31⋊C5))⋊C3

Splittings

Fitting, socleC2×C3×C5×C31 ⋊ C2×C3×C5
derivedC5×C31 ⋊ C22×C32×C5
HallC3×C5×(C31⋊C3)⋊C5 ⋊ C22
HallC2×C5⋊(D31⋊C5) ⋊ C32
HallC5×ΓL(1,𝔽32) ⋊ C22×C32
HallC3×C31⋊C3 ⋊ C2×C5×D5
SylowC31 ⋊ C2×C32×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊AGL(1,𝔽31)
commutator, cosocle, hypocenterC5×C31C22×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C31C2×C3×C5
LCSG ▷ C5×C31
UCSC1 ◁ C2×C3

288 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 439);