Finite Group Databasebeta

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C19×Dic195 #28414733

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

Aliases

direct productC19×Dic195
unambiguous semidirect productC3⋊(C19×Dic65)

Splittings

derived, HallC3×C5×C13 ⋊ C4×C19
HallC3×C5×C13×C19 ⋊ C4
HallC5×C13×C19 ⋊ Dic3
HallC3×C13×C19 ⋊ Dic5
HallC3×C5×C19 ⋊ Dic13
HallC13×C19 ⋊ Dic15
HallC5×C19 ⋊ Dic39
HallC5×C13 ⋊ Dic3×C19
HallC3×C19 ⋊ Dic65
HallC3×C13 ⋊ C19×Dic5
HallC3×C5 ⋊ C19×Dic13
SylowC13 ⋊ C19×Dic15
SylowC5 ⋊ C19×Dic39
SylowC3 ⋊ C19×Dic65

Subgroups

subgroupG/H
center, hypercenterC2×C19D195
commutator, hypocenterC3×C5×C13C4×C19
FrattiniC2C19×D195
Fitting, socle, prime radicalC2×C3×C5×C13×C19C2
cosocleC2×C3×C5×C13C2×C19
LCSG ▷ C3×C5×C13
UCSC1 ◁ C2×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14820

Conjugacy classes & character table

3762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 19);