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C2×D9×C31⋊C25 #42124282

order27900
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×D9×C31⋊C25
unambiguous semidirect productC9⋊(C22×C31⋊C25)
unambiguous semidirect product(C2×C9)⋊(C2×C31⋊C25)
unambiguous semidirect product(C2×D9×C31)⋊C25

Splittings

derived, HallC9×C31 ⋊ C22×C25
HallC9×C31⋊C25 ⋊ C22
HallC2×D9×C31 ⋊ C25
SylowC31 ⋊ C2×D9×C25
SylowC9 ⋊ C22×C31⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5D9×ΓL(1,𝔽32)
commutator, hypocenterC9×C31C22×C25
FrattiniC3×C5C2×D3×ΓL(1,𝔽32)
FittingC2×C5×C9×C31C2×C5
socleC2×C3×C5×C31C5×D3
prime radicalC2×C5×D9×C31C5
cosocleC5×C9×C31C22×C5
LCSG ▷ C9×C31
UCSC1 ◁ C2×C5

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 29);