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C19×C3⋊#63118 #28414904

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

Aliases

direct productC19×C3⋊#63118
unambiguous semidirect productC3⋊(C19×#63118)

Splittings

Fitting, socle, HallC3×C5×C13×C19 ⋊ C4
derived, HallC3×C5×C13 ⋊ C4×C19
HallC5×C13×C19 ⋊ Dic3
HallC3×C13×C19 ⋊ Dic5
HallC3×C5×C19 ⋊ #261
HallC13×C19 ⋊ Dic15
HallC5×C19 ⋊ C3⋊#261
HallC5×C13 ⋊ Dic3×C19
HallC3×C19 ⋊ #63118
HallC3×C13 ⋊ C19×Dic5
HallC3×C5 ⋊ C19×#261
SylowC13 ⋊ C19×Dic15
SylowC5 ⋊ C19×C3⋊#261
SylowC3 ⋊ C19×#63118

Subgroups

subgroupG/H
center, hypercenterC19C3⋊#63118
commutator, hypocenterC3×C5×C13C4×C19
FrattiniC1G
Fitting, socleC3×C5×C13×C19C4
prime radicalC3×C5×C19×D13C2
cosocleC3×C5×D13C2×C19
LCSG ▷ C3×C5×C13
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3705

Conjugacy classes & character table

1197 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 190);