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C2×C3×C11×C5⋊(D13⋊C3) #38788130

order25740
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C11×C5⋊(D13⋊C3)
unambiguous semidirect product(C2×C5)⋊(C3×C11×D13⋊C3)
unambiguous semidirect product(C2×C13⋊C3)⋊(C3×D5×C11)
unambiguous semidirect product(C2×D65)⋊(C32×C11)
unambiguous semidirect product(C2×C3×D65)⋊(C3×C11)
unambiguous semidirect product(C2×C11×D65)⋊C32
unambiguous semidirect product(C2×C3×C11×D65)⋊C3

Splittings

Fitting, socleC2×C3×C5×C11×C13 ⋊ C2×C3
derived, HallC5×C13 ⋊ C22×C32×C11
HallC3×C5×C11×C13⋊C3 ⋊ C22
HallC2×C11×D65 ⋊ C32
HallC3×C11×C13⋊C3 ⋊ C2×D5
HallC5×C11×C13 ⋊ C22×C32
HallC3×C5×C13⋊C3 ⋊ C22×C11
HallC2×D65 ⋊ C32×C11
HallC11×C13 ⋊ C2×C32×D5
HallC3×C13⋊C3 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×C3×D13⋊C3
SylowC13 ⋊ C2×C32×D5×C11
SylowC5 ⋊ C2×C3×C11×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11C5⋊(D13⋊C3)
commutator, cosocle, hypocenterC5×C13C22×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C13C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C11

240 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 4290

Conjugacy classes & character table

1452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 361);