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C3×C3⋊(C11⋊(C11⋊AGL(1,𝔽5))) #36345307

order21780
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C11

Aliases

direct productC3×C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))
unambiguous semidirect productC3⋊(C3×C11⋊(C11⋊AGL(1,𝔽5)))
unambiguous semidirect productC11⋊(C3×C3⋊(C11⋊AGL(1,𝔽5)))

Splittings

Fitting, socle, HallC32×C5×C112 ⋊ C4
derivedC3×C5×C112 ⋊ C3×C4
HallC32×C112 ⋊ AGL(1,𝔽5)
HallC5×C112 ⋊ C3×Dic3
SylowC112 ⋊ C3×ΓL(1,𝔽16)
HallC32×C5 ⋊ C11⋊Dic11
SylowC32 ⋊ C11⋊(C11⋊AGL(1,𝔽5))
SylowC5 ⋊ C3×C3⋊(C11⋊Dic11)

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))
commutator, hypocenterC3×C5×C112C3×C4
FrattiniC1G
Fitting, socleC32×C5×C112C4
prime radicalC32×D5×C112C2
cosocleC3×D5×C112C2×C3
LCSG ▷ C3×C5×C112
UCSC1 ◁ C3

392 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2187 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 656);