Finite Group Databasebeta

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C3×C19⋊#10596816 #45683298

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

Aliases

direct productC3×C19⋊#10596816

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 ⋊ Dic29
HallC5×C29 ⋊ C3×Dic19
HallC5×C19 ⋊ C3×Dic29
HallC3×C29 ⋊ C19⋊AGL(1,𝔽5)
HallC3×C19 ⋊ #10596816
SylowC29 ⋊ C3×C19⋊AGL(1,𝔽5)
SylowC19 ⋊ C3×#10596816
HallC3×C5 ⋊ Dic551
SylowC5 ⋊ C3×Dic551

Subgroups

subgroupG/H
center, hypercenterC3C19⋊#10596816
commutator, hypocenterC5×C19×C29C3×C4
FrattiniC1G
Fitting, socleC3×C5×C19×C29C4
prime radicalC3×D5×C19×C29C2
cosocleD5×C19×C29C2×C3
LCSG ▷ C5×C19×C29
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8265

Conjugacy classes & character table

3315 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 62);