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C3×C5×(C11⋊Dic11)⋊C3 #36345012

order21780
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3×C11

Aliases

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

Splittings

derived, SylowC112 ⋊ C32×C4×C5
HallC3×C5×C112⋊C3 ⋊ C4
HallC5×C11⋊Dic11 ⋊ C32
HallC3×C112⋊C3 ⋊ C4×C5
HallC5×C112 ⋊ C32×C4
HallC11⋊Dic11 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5(C11⋊D11)⋊C3
commutator, hypocenterC112C32×C4×C5
FrattiniC2C3×C5×(C11⋊D11)⋊C3
Fitting, socleC2×C3×C5×C112C2×C3
prime radicalC2×C3×C5×C112⋊C3C2
cosocleC2×C112C2×C32×C5
LCSG ▷ C112
UCSC1 ◁ C2×C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 361);