Finite Group Databasebeta

← Prev (#36345013) Next (#36345015) →

C3×(C11⋊Dic55)⋊C3 #36345014

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

Aliases

direct productC3×(C11⋊Dic55)⋊C3
unambiguous semidirect product(C11⋊Dic55)⋊C32
unambiguous semidirect product(C3×C11⋊Dic55)⋊C3

Splittings

derived, HallC5×C112 ⋊ C32×C4
HallC3×C5×C112⋊C3 ⋊ C4
HallC11⋊Dic55 ⋊ C32
HallC3×C112⋊C3 ⋊ Dic5
SylowC112 ⋊ C32×Dic5
SylowC5 ⋊ C3×(C11⋊Dic11)⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊((C11⋊D11)⋊C3)
commutator, hypocenterC5×C112C32×C4
FrattiniC2C3×C5⋊((C11⋊D11)⋊C3)
Fitting, socleC2×C3×C5×C112C2×C3
prime radicalC2×C3×C5×C112⋊C3C2
cosocleC2×C5×C112C2×C32
LCSG ▷ C5×C112
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

672 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 363);