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C2×C19⋊C3×D65 #28414867

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

Aliases

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

Splittings

Fitting, socleC2×C5×C13×C19 ⋊ C2×C3
derived, HallC5×C13×C19 ⋊ C22×C3
HallC2×C19×D65 ⋊ 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 ⋊ C22×C19⋊C3
SylowC19 ⋊ C2×C3×D65
SylowC13 ⋊ C2×D5×C19⋊C3
SylowC5 ⋊ C2×D13×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C19⋊C3×D65
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 153);