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C2×D5×C29×C13⋊C3 #36383136

order22620
automorphism?
homologyAbelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C29×C13⋊C3
unambiguous semidirect productC5⋊(C22×C29×C13⋊C3)
unambiguous semidirect product(C2×C5)⋊(C2×C29×C13⋊C3)
unambiguous semidirect product(C2×D5×C13)⋊(C3×C29)
unambiguous semidirect product(C2×D5×C13×C29)⋊C3

Splittings

Fitting, socleC2×C5×C13×C29 ⋊ C2×C3
derived, HallC5×C13 ⋊ C22×C3×C29
HallC2×D5×C13×C29 ⋊ C3
HallC5×C29×C13⋊C3 ⋊ C22
HallC5×C13×C29 ⋊ C22×C3
HallC13×C29 ⋊ C2×C3×D5
HallC2×D5×C13 ⋊ C3×C29
HallC5×C13⋊C3 ⋊ C22×C29
HallC5×C29 ⋊ C22×C13⋊C3
SylowC13 ⋊ C2×C3×D5×C29
SylowC5 ⋊ C22×C29×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C29D5×C13⋊C3
commutator, cosocle, hypocenterC5×C13C22×C3×C29
FrattiniC1G
Fitting, socleC2×C5×C13×C29C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C2×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3770

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22620, 66);