Finite Group Databasebeta

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C3×((C11⋊Dic11)⋊C3)⋊C5 #36344965

order21780
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×((C11⋊Dic11)⋊C3)⋊C5
unambiguous semidirect product((C11⋊Dic11)⋊C3)⋊(C3×C5)
unambiguous semidirect product#14559051⋊C32
unambiguous semidirect product(C3×(C11⋊Dic11)⋊C3)⋊C5
unambiguous semidirect product(C3×#14559051)⋊C3

Splittings

derived, SylowC112 ⋊ C32×C4×C5
HallC3×(C112⋊C3)⋊C5 ⋊ C4
HallC3×(C11⋊Dic11)⋊C3 ⋊ C5
Hall#14559051 ⋊ C32
HallC3×C112⋊C3 ⋊ C4×C5
Hall#10597243 ⋊ C32×C4
HallC11⋊Dic11 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3((C11⋊D11)⋊C3)⋊C5
commutator, hypocenterC112C32×C4×C5
FrattiniC2C3×((C11⋊D11)⋊C3)⋊C5
Fitting, socleC2×C3×C112C2×C3×C5
prime radicalC2×C3×(C112⋊C3)⋊C5C2
cosocleC2×C112C2×C32×C5
LCSG ▷ C112
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 314);