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C61×C9⋊AGL(1,𝔽5) #24926701

order10980
isoclinismisoclinic class of C9⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C61 · Schur multiplier (H2) = C1

Aliases

direct productC61×C9⋊AGL(1,𝔽5)
unambiguous semidirect productC9⋊(AGL(1,𝔽5)×C61)

Splittings

Fitting, HallC5×C9×C61 ⋊ C4
derived, HallC5×C9 ⋊ C4×C61
HallC9×C61 ⋊ AGL(1,𝔽5)
HallC5×C61 ⋊ Dic9
SylowC9 ⋊ AGL(1,𝔽5)×C61
SylowC5 ⋊ Dic9×C61

Subgroups

subgroupG/H
center, hypercenterC61C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C61
FrattiniC3ΓL(1,𝔽16)×C61
FittingC5×C9×C61C4
socleC3×C5×C61Dic3
prime radicalC3×D5×C61D3
cosocleC9×D5C2×C61
LCSG ▷ C5×C9
UCSC1 ◁ C61

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1281 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 51);