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C2×C5×C9⋊(D31⋊C5) #42124518

order27900
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5×C9⋊(D31⋊C5)
unambiguous semidirect product(C2×C9)⋊(C5×D31⋊C5)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C5×D9)
unambiguous semidirect product(C2×D279)⋊C52
unambiguous semidirect product(C2×C5×D279)⋊C5

Splittings

FittingC2×C5×C9×C31 ⋊ C2×C5
derived, HallC9×C31 ⋊ C22×C52
HallC5×C9×ΓL(1,𝔽32) ⋊ C22
HallC2×D279 ⋊ C52
HallC5×ΓL(1,𝔽32) ⋊ C2×D9
SylowC31 ⋊ C2×C52×D9
SylowC9 ⋊ C2×C5×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C5C9⋊(D31⋊C5)
commutator, cosocle, hypocenterC9×C31C22×C52
FrattiniC3C2×C5×C3⋊(D31⋊C5)
FittingC2×C5×C9×C31C2×C5
socleC2×C3×C5×C31C5×D3
LCSG ▷ C9×C31
UCSC1 ◁ C2×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 265);