Finite Group Databasebeta

← Prev (#44568412) Next (#44568414) →

D3×D2695 #44568413

order32340
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD3×D2695
unambiguous semidirect product(C5×D3)⋊D539
unambiguous semidirect product(D3×C11)⋊D245
unambiguous semidirect product(D3×C49)⋊D55

Splittings

Fitting, derived, HallC3×C5×C11×C49 ⋊ C22
HallC5×C11×C49 ⋊ C2×D3
HallC3×C11×C49 ⋊ C2×D5
HallC3×C5×C49 ⋊ C2×D11
HallC11×C49 ⋊ D3×D5
HallC5×C49 ⋊ D3×D11
HallC3×C5×C11 ⋊ C2×D49
HallC3×C49 ⋊ C2×D55
HallC5×C11 ⋊ D3×D49
SylowC49 ⋊ D3×D55
HallC3×C11 ⋊ C2×D245
HallC3×C5 ⋊ C2×D539
SylowC11 ⋊ D3×D245
SylowC5 ⋊ D3×D539
SylowC3 ⋊ C2×D2695

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C5×C11×C49C22
FrattiniC7D3×D385
socleC3×C5×C7×C11C2×D7
LCSG ▷ C3×C5×C11×C49
UCSC1

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4047 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 115);