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C2×C72×C5⋊(D13⋊C3) #50304274

order38220
automorphism?
homologyAbelianization (H1) = C22×C3×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C72×C5⋊(D13⋊C3)
unambiguous semidirect product(C2×C5)⋊(C72×D13⋊C3)
unambiguous semidirect product(C2×C13⋊C3)⋊(C72×D5)
unambiguous semidirect product(C2×D65)⋊(C3×C72)

Splittings

Fitting, socleC2×C5×C72×C13 ⋊ C2×C3
derived, HallC5×C13 ⋊ C22×C3×C72
HallC2×C72×D65 ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C22
HallC5×C72×C13 ⋊ C22×C3
HallC72×C13⋊C3 ⋊ C2×D5
HallC72×C13 ⋊ C2×C3×D5
HallC2×D65 ⋊ C3×C72
HallC5×C72 ⋊ C2×D13⋊C3
HallC5×C13⋊C3 ⋊ C22×C72
HallC13⋊C3 ⋊ C2×C72×D5
SylowC13 ⋊ C2×C3×C72×D5
SylowC5 ⋊ C2×C72×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C72C5⋊(D13⋊C3)
commutator, cosocle, hypocenterC5×C13C22×C3×C72
FrattiniC1G
Fitting, socleC2×C5×C72×C13C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C2×C72

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6370

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 960);