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C5×C3⋊(C19⋊#261) #28414889

order14820
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(C19⋊#261)
unambiguous semidirect productC3⋊(C5×C19⋊#261)
unambiguous semidirect productC19⋊(C5×C3⋊#261)

Splittings

Fitting, socle, HallC3×C5×C13×C19 ⋊ C4
derived, HallC3×C13×C19 ⋊ C4×C5
HallC5×C13×C19 ⋊ Dic3
HallC3×C5×C19 ⋊ #261
HallC13×C19 ⋊ C5×Dic3
HallC3×C5×C13 ⋊ Dic19
HallC5×C19 ⋊ C3⋊#261
HallC5×C13 ⋊ Dic57
HallC3×C19 ⋊ C5×#261
HallC3×C13 ⋊ C5×Dic19
SylowC19 ⋊ C5×C3⋊#261
HallC3×C5 ⋊ C19⋊#261
SylowC13 ⋊ C5×Dic57
SylowC3 ⋊ C5×C19⋊#261

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C19⋊#261)
commutator, hypocenterC3×C13×C19C4×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C19C4
prime radicalC3×C5×C19×D13C2
cosocleC3×C19×D13C2×C5
LCSG ▷ C3×C13×C19
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3705

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 175);