Finite Group Databasebeta

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C3×Dic3×C121⋊C5 #36344692

order21780
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C121⋊C5
unambiguous semidirect productC3⋊(C3×C4×C121⋊C5)
unambiguous semidirect product(Dic3×C121)⋊(C3×C5)
unambiguous semidirect product(C3×Dic3×C121)⋊C5

Splittings

derivedC3×C121 ⋊ C3×C4×C5
HallC32×C121⋊C5 ⋊ C4
HallC3×Dic3×C121 ⋊ C5
HallC32×C121 ⋊ C4×C5
SylowC121 ⋊ C3×C5×Dic3
SylowC32 ⋊ C4×C121⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×C121⋊C5
commutator, hypocenterC3×C121C3×C4×C5
FrattiniC2×C11C3×D3×C11⋊C5
FittingC2×C32×C121C2×C5
socleC2×C32×C11C2×C11⋊C5
prime radicalC2×C32×C121⋊C5C2
cosocleC2×C3×C121C2×C3×C5
LCSG ▷ C3×C121
UCSC1 ◁ C2×C3

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

522 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 41);