Finite Group Databasebeta

← Prev (#26014443) Next (#26014445) →

C2×C3×C5×C11×D17 #26014444

order11220
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C11×D17
unambiguous semidirect productC17⋊(C22×C3×C5×C11)
unambiguous semidirect product(C2×C17)⋊(C2×C3×C5×C11)

Splittings

Fitting, socleC2×C3×C5×C11×C17 ⋊ C2
derived, SylowC17 ⋊ C22×C3×C5×C11
HallC3×C5×C11×C17 ⋊ C22
HallC5×C11×C17 ⋊ C22×C3
HallC3×C11×C17 ⋊ C22×C5
HallC3×C5×C17 ⋊ C22×C11
HallC11×C17 ⋊ C22×C3×C5
HallC5×C17 ⋊ C22×C3×C11
HallC3×C17 ⋊ C22×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11D17
commutator, cosocle, hypocenterC17C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C17C2
LCSG ▷ C17
UCSC1 ◁ C2×C3×C5×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C9×C11×D17, C3×C5×D3×C11×D17, C2×C32×C5×C11×D17, …
maximal normal subgroup ofC2×C5×C9×C11×D17, C2×C32×C5×C11×D17
maximal quotient ofC2×C5×C9×C11×D17, C3×C5×D3×C11×D17, C2×C32×C5×C11×D17, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 120);