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C5×AGL(1,𝔽5)×C31⋊C9 #42124491

order27900
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽5)×C31⋊C9
unambiguous semidirect product(C5×AGL(1,𝔽5)×C31)⋊C9

Splittings

derivedC5×C31 ⋊ C4×C5×C9
HallC52×C31⋊C9 ⋊ C4
HallC5×AGL(1,𝔽5)×C31 ⋊ C9
HallC52×C31 ⋊ C4×C9
SylowC31 ⋊ C5×C9×AGL(1,𝔽5)
SylowC52 ⋊ C4×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5AGL(1,𝔽5)×C31⋊C3
commutator, hypocenterC5×C31C4×C5×C9
FrattiniC3C5×AGL(1,𝔽5)×C31⋊C3
Fitting, socleC3×C52×C31C3×C4
prime radicalC3×C5×D5×C31C2×C3
cosocleC3×D5×C31C2×C3×C5
LCSG ▷ C5×C31
UCSC1 ◁ C3×C5

78 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

975 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 238);