Finite Group Databasebeta

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C19×Dic65⋊C3 #28414756

order14820
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×Dic65⋊C3
unambiguous semidirect productDic65⋊(C3×C19)

Splittings

derived, HallC5×C13 ⋊ C3×C4×C19
HallC19×Dic65 ⋊ C3
HallC5×C19×C13⋊C3 ⋊ C4
HallC5×C13×C19 ⋊ C3×C4
HallC19×C13⋊C3 ⋊ Dic5
HallDic65 ⋊ C3×C19
HallC13×C19 ⋊ C3×Dic5
HallC5×C13⋊C3 ⋊ C4×C19
HallC5×C19 ⋊ Dic13⋊C3
HallC13⋊C3 ⋊ C19×Dic5
SylowC13 ⋊ C3×C19×Dic5
SylowC5 ⋊ C19×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C19C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C3×C4×C19
FrattiniC2C19×C5⋊(D13⋊C3)
Fitting, socleC2×C5×C13×C19C2×C3
prime radicalC2×C5×C19×C13⋊C3C2
cosocleC2×C5×C13C2×C3×C19
LCSG ▷ C5×C13
UCSC1 ◁ C2×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4940

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 42);