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C3×C19⋊#63122 #28414874

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

Aliases

direct productC3×C19⋊#63122

Splittings

Fitting, socle, HallC3×C5×C13×C19 ⋊ C4
derived, HallC5×C13×C19 ⋊ C3×C4
HallC3×C13×C19 ⋊ AGL(1,𝔽5)
HallC3×C5×C19 ⋊ #261
HallC13×C19 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C13 ⋊ Dic19
HallC5×C19 ⋊ C3×#261
HallC5×C13 ⋊ C3×Dic19
HallC3×C19 ⋊ #63122
HallC3×C13 ⋊ C19⋊AGL(1,𝔽5)
SylowC19 ⋊ C3×#63122
HallC3×C5 ⋊ C19⋊#261
SylowC13 ⋊ C3×C19⋊AGL(1,𝔽5)
SylowC5 ⋊ C3×C19⋊#261

Subgroups

subgroupG/H
center, hypercenterC3C19⋊#63122
commutator, hypocenterC5×C13×C19C3×C4
FrattiniC1G
Fitting, socleC3×C5×C13×C19C4
prime radicalC3×C19×D65C2
cosocleC19×D65C2×C3
LCSG ▷ C5×C13×C19
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3705

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 160);