Finite Group Databasebeta

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C3×C19×AGL(1,𝔽5)×C29 #45683291

order33060
automorphism?
homologyAbelianization (H1) = C3×C4×C19×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19×AGL(1,𝔽5)×C29

Splittings

Fitting, socle, HallC3×C5×C19×C29 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C19×C29
HallC5×C19×C29 ⋊ C3×C4
HallC3×C5×C29 ⋊ C4×C19
HallC3×C5×C19 ⋊ C4×C29
HallC5×C29 ⋊ C3×C4×C19
HallC5×C19 ⋊ C3×C4×C29
HallC3×C5 ⋊ C4×C19×C29

Subgroups

subgroupG/H
center, hypercenterC3×C19×C29AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C19×C29
FrattiniC1G
Fitting, socleC3×C5×C19×C29C4
prime radicalC3×D5×C19×C29C2
cosocleD5C2×C3×C19×C29
LCSG ▷ C5
UCSC1 ◁ C3×C19×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8265

Conjugacy classes & character table

8265 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 55);