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C3×(C11⋊(C11⋊AGL(1,𝔽5)))⋊C3 #36345184

order21780
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C11

Aliases

direct productC3×(C11⋊(C11⋊AGL(1,𝔽5)))⋊C3
unambiguous semidirect product(C11⋊(C11⋊AGL(1,𝔽5)))⋊C32
unambiguous semidirect product(C3×C11⋊(C11⋊AGL(1,𝔽5)))⋊C3

Splittings

Fitting, socleC3×C5×C112 ⋊ C3×C4
derived, HallC5×C112 ⋊ C32×C4
HallC3×C5×C112⋊C3 ⋊ C4
HallC11⋊(C11⋊AGL(1,𝔽5)) ⋊ C32
HallC3×C112⋊C3 ⋊ AGL(1,𝔽5)
SylowC112 ⋊ C32×AGL(1,𝔽5)
SylowC5 ⋊ C3×(C11⋊Dic11)⋊C3

Subgroups

subgroupG/H
center, hypercenterC3(C11⋊(C11⋊AGL(1,𝔽5)))⋊C3
commutator, hypocenterC5×C112C32×C4
FrattiniC1G
Fitting, socleC3×C5×C112C3×C4
prime radicalC3×D5×C112⋊C3C2
cosocleD5×C112C2×C32
LCSG ▷ C5×C112
UCSC1 ◁ C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

285 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 533);