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C2×C5⋊((C19⋊C3)⋊D13) #28414866

order14820
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊((C19⋊C3)⋊D13)
unambiguous semidirect product(C2×C5)⋊((C19⋊C3)⋊D13)
unambiguous semidirect product(C2×C19⋊C3)⋊D65

Splittings

Fitting, socleC2×C5×C13×C19 ⋊ C2×C3
derived, HallC5×C13×C19 ⋊ C22×C3
HallC2×D1235 ⋊ C3
HallC5×C13×C19⋊C3 ⋊ C22
HallC13×C19⋊C3 ⋊ C2×D5
HallC5×C19⋊C3 ⋊ C2×D13
HallC13×C19 ⋊ C2×C3×D5
HallC5×C19 ⋊ C2×C3×D13
HallC5×C13 ⋊ C2×D19⋊C3
HallC19⋊C3 ⋊ C2×D65
SylowC19 ⋊ C2×C3×D65
SylowC13 ⋊ C2×C5⋊(D19⋊C3)
SylowC5 ⋊ C2×(C19⋊C3)⋊D13

Subgroups

subgroupG/H
center, hypercenterC2C5⋊((C19⋊C3)⋊D13)
commutator, cosocle, hypocenterC5×C13×C19C22×C3
FrattiniC1G
Fitting, socleC2×C5×C13×C19C2×C3
LCSG ▷ C5×C13×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2470

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 152);