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C112×C9⋊AGL(1,𝔽5) #36344930

order21780
isoclinismisoclinic class of C9⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C112 · Schur multiplier (H2) = C11

Aliases

direct productC112×C9⋊AGL(1,𝔽5)
unambiguous semidirect productC9⋊(C112×AGL(1,𝔽5))

Splittings

Fitting, HallC5×C9×C112 ⋊ C4
derived, HallC5×C9 ⋊ C4×C112
HallC9×C112 ⋊ AGL(1,𝔽5)
HallC5×C112 ⋊ Dic9
SylowC9 ⋊ C112×AGL(1,𝔽5)
SylowC5 ⋊ C112×Dic9

Subgroups

subgroupG/H
center, hypercenterC112C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C112
FrattiniC3C112×ΓL(1,𝔽16)
FittingC5×C9×C112C4
socleC3×C5×C112Dic3
prime radicalC3×D5×C112D3
cosocleC9×D5C2×C112
LCSG ▷ C5×C9
UCSC1 ◁ C112

252 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2541 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 279);