Finite Group Databasebeta

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C9⋊AGL(1,𝔽5)×C181 #45656380

order32580
isoclinismisoclinic class of C9⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C181 · Schur multiplier (H2) = C1

Aliases

direct productC9⋊AGL(1,𝔽5)×C181
unambiguous semidirect productC9⋊(AGL(1,𝔽5)×C181)

Splittings

Fitting, HallC5×C9×C181 ⋊ C4
derived, HallC5×C9 ⋊ C4×C181
HallC9×C181 ⋊ AGL(1,𝔽5)
HallC5×C181 ⋊ Dic9
SylowC9 ⋊ AGL(1,𝔽5)×C181
SylowC5 ⋊ Dic9×C181

Subgroups

subgroupG/H
center, hypercenterC181C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C181
FrattiniC3ΓL(1,𝔽16)×C181
FittingC5×C9×C181C4
socleC3×C5×C181Dic3
prime radicalC3×D5×C181D3
cosocleC9×D5C2×C181
LCSG ▷ C5×C9
UCSC1 ◁ C181

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3801 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 51);