Finite Group Databasebeta

← Prev (#26014342) Next (#26014344) →

C3×C17×Dic11⋊C5 #26014343

order11220
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×Dic11⋊C5
unambiguous semidirect productDic11⋊(C3×C5×C17)
unambiguous semidirect product(C11⋊C5)⋊(C3×C4×C17)
unambiguous semidirect product(C3×Dic11)⋊(C5×C17)
unambiguous semidirect product(C17×Dic11)⋊(C3×C5)
unambiguous semidirect product(C3×C17×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C3×C4×C5×C17
HallC3×C17×C11⋊C5 ⋊ C4
HallC3×C17×Dic11 ⋊ C5
HallC17×C11⋊C5 ⋊ C3×C4
HallC17×Dic11 ⋊ C3×C5
HallC3×C11×C17 ⋊ C4×C5
HallC11×C17 ⋊ C3×C4×C5
HallC3×C11⋊C5 ⋊ C4×C17
HallC3×Dic11 ⋊ C5×C17
HallC11⋊C5 ⋊ C3×C4×C17
HallDic11 ⋊ C3×C5×C17
HallC3×C11 ⋊ C4×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17AGL(1,𝔽11)
commutator, hypocenterC11C3×C4×C5×C17
FrattiniC2C3×C17×AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C17C2×C5
prime radicalC2×C3×C17×C11⋊C5C2
cosocleC2×C11C2×C3×C5×C17
LCSG ▷ C11
UCSC1 ◁ C2×C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C17×Dic11⋊C5, C32×C17×Dic11⋊C5, C3×C17×C3⋊(Dic11⋊C5)
maximal normal subgroup ofC9×C17×Dic11⋊C5, C32×C17×Dic11⋊C5
maximal quotient ofC9×C17×Dic11⋊C5, C32×C17×Dic11⋊C5, C3×C17×C3⋊(Dic11⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 19);