Finite Group Databasebeta

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C3×C19⋊#10596815 #45683297

order33060
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19⋊#10596815

Splittings

Fitting, socle, HallC3×C5×C19×C29 ⋊ C4
derived, HallC5×C19×C29 ⋊ C3×C4
HallC3×C19×C29 ⋊ AGL(1,𝔽5)
HallC19×C29 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C29 ⋊ Dic19
HallC3×C5×C19 ⋊ #1181
HallC5×C29 ⋊ C3×Dic19
HallC5×C19 ⋊ C3×#1181
HallC3×C29 ⋊ C19⋊AGL(1,𝔽5)
HallC3×C19 ⋊ #10596815
SylowC29 ⋊ C3×C19⋊AGL(1,𝔽5)
SylowC19 ⋊ C3×#10596815
HallC3×C5 ⋊ C19⋊#1181
SylowC5 ⋊ C3×C19⋊#1181

Subgroups

subgroupG/H
center, hypercenterC3C19⋊#10596815
commutator, hypocenterC5×C19×C29C3×C4
FrattiniC1G
Fitting, socleC3×C5×C19×C29C4
prime radicalC3×C19×D145C2
cosocleC19×D145C2×C3
LCSG ▷ C5×C19×C29
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8265

Conjugacy classes & character table

2118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 61);