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C9×AGL(1,𝔽5)×C181 #45656372

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

Aliases

direct productC9×AGL(1,𝔽5)×C181

Splittings

Fitting, HallC5×C9×C181 ⋊ C4
derived, SylowC5 ⋊ C4×C9×C181
HallC5×C181 ⋊ C4×C9
HallC5×C9 ⋊ C4×C181

Subgroups

subgroupG/H
center, hypercenterC9×C181AGL(1,𝔽5)
commutator, hypocenterC5C4×C9×C181
FrattiniC3C3×AGL(1,𝔽5)×C181
FittingC5×C9×C181C4
socleC3×C5×C181C3×C4
prime radicalC3×D5×C181C2×C3
cosocleC3×D5C2×C3×C181
LCSG ▷ C5
UCSC1 ◁ C9×C181

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 43);