Finite Group Databasebeta

← Prev (#27160100) Next (#27160102) →

C2×C5×D3×C11×C19 #27160101

order12540
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C22×C5×C11×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D3×C11×C19
unambiguous semidirect productC3⋊(C22×C5×C11×C19)
unambiguous semidirect product(C2×C3)⋊(C2×C5×C11×C19)

Splittings

Fitting, socleC2×C3×C5×C11×C19 ⋊ C2
derived, SylowC3 ⋊ C22×C5×C11×C19
HallC3×C5×C11×C19 ⋊ C22
HallC3×C11×C19 ⋊ C22×C5
HallC3×C5×C19 ⋊ C22×C11
HallC3×C5×C11 ⋊ C22×C19
HallC3×C19 ⋊ C22×C5×C11
HallC3×C11 ⋊ C22×C5×C19
HallC3×C5 ⋊ C22×C11×C19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11×C19D3
commutator, cosocle, hypocenterC3C22×C5×C11×C19
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C19C2
LCSG ▷ C3
UCSC1 ◁ C2×C5×C11×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6270 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C11×D9×C19, C2×C5×D3×C11×C19⋊C3, C5×D32×C11×C19, …
maximal normal subgroup ofC2×C5×D3×C11×C19⋊C3, C2×C3×C5×D3×C11×C19
maximal quotient ofC2×C5×C11×D9×C19, C5×D32×C11×C19, C2×C3×C5×D3×C11×C19, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12540, 131);