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C2×C9×D5×ΓL(1,𝔽32) #42124517

order27900
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D5×ΓL(1,𝔽32)
unambiguous semidirect productC5⋊(C22×C9×ΓL(1,𝔽32))
unambiguous semidirect product(C2×C5)⋊(C2×C9×ΓL(1,𝔽32))
unambiguous semidirect product(C2×C9×D5×C31)⋊C5

Splittings

FittingC2×C5×C9×C31 ⋊ C2×C5
derivedC5×C31 ⋊ C22×C5×C9
HallC5×C9×ΓL(1,𝔽32) ⋊ C22
HallC5×ΓL(1,𝔽32) ⋊ C22×C9
HallC9×C31 ⋊ C2×C5×D5
SylowC31 ⋊ C2×C5×C9×D5

Subgroups

subgroupG/H
center, hypercenterC2×C9D5×ΓL(1,𝔽32)
commutator, hypocenterC5×C31C22×C5×C9
FrattiniC3C2×C3×D5×ΓL(1,𝔽32)
FittingC2×C5×C9×C31C2×C5
socleC2×C3×C5×C31C2×C3×C5
prime radicalC2×C3×D5×ΓL(1,𝔽32)C3
cosocleC3×C5×C31C22×C3×C5
LCSG ▷ C5×C31
UCSC1 ◁ C2×C9

144 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 63 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

792 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 264);