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C59×C9⋊AGL(1,𝔽5) #24902871

order10620
isoclinismisoclinic class of C9⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C59 · Schur multiplier (H2) = C1

Aliases

direct productC59×C9⋊AGL(1,𝔽5)
unambiguous semidirect productC9⋊(AGL(1,𝔽5)×C59)

Splittings

Fitting, HallC5×C9×C59 ⋊ C4
derived, HallC5×C9 ⋊ C4×C59
HallC9×C59 ⋊ AGL(1,𝔽5)
HallC5×C59 ⋊ Dic9
SylowC9 ⋊ AGL(1,𝔽5)×C59
SylowC5 ⋊ Dic9×C59

Subgroups

subgroupG/H
center, hypercenterC59C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C59
FrattiniC3C59×ΓL(1,𝔽16)
FittingC5×C9×C59C4
socleC3×C5×C59Dic3
prime radicalC3×D5×C59D3
cosocleC9×D5C2×C59
LCSG ▷ C5×C9
UCSC1 ◁ C59

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1239 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10620, 14);