Finite Group Databasebeta

← Prev (#36344977) Next (#36344979) →

C32×(C11⋊C5)⋊Dic11 #36344978

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

Aliases

direct productC32×(C11⋊C5)⋊Dic11
unambiguous semidirect product(C11⋊C5)⋊(C32×Dic11)

Splittings

derived, SylowC112 ⋊ C32×C4×C5
HallC32×C11×C11⋊C5 ⋊ C4
HallC32×C11⋊Dic11 ⋊ C5
HallC32×C112 ⋊ C4×C5
HallC11×C11⋊C5 ⋊ C32×C4
HallC11⋊Dic11 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32(C11⋊C5)⋊D11
commutator, hypocenterC112C32×C4×C5
FrattiniC2C32×(C11⋊C5)⋊D11
Fitting, socleC2×C32×C112C2×C5
prime radicalC2×C32×C11×C11⋊C5C2
cosocleC2×C112C2×C32×C5
LCSG ▷ C112
UCSC1 ◁ C2×C32

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

828 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 327);