Finite Group Databasebeta

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C5×C29×Dic57 #45683248

order33060
automorphism?
homologyAbelianization (H1) = C4×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29×Dic57
unambiguous semidirect productC3⋊(C5×C29×Dic19)
unambiguous semidirect productC19⋊(C5×Dic3×C29)

Splittings

derived, HallC3×C19 ⋊ C4×C5×C29
HallC3×C5×C19×C29 ⋊ C4
HallC5×C19×C29 ⋊ Dic3
HallC3×C19×C29 ⋊ C4×C5
HallC19×C29 ⋊ C5×Dic3
HallC3×C5×C29 ⋊ Dic19
HallC3×C5×C19 ⋊ C4×C29
HallC5×C19 ⋊ Dic3×C29
HallC3×C29 ⋊ C5×Dic19
SylowC19 ⋊ C5×Dic3×C29
HallC3×C5 ⋊ C29×Dic19
SylowC3 ⋊ C5×C29×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C29D57
commutator, hypocenterC3×C19C4×C5×C29
FrattiniC2C5×C29×D57
Fitting, socle, prime radicalC2×C3×C5×C19×C29C2
cosocleC2×C3×C19C2×C5×C29
LCSG ▷ C3×C19
UCSC1 ◁ C2×C5×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33060

Conjugacy classes & character table

8700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 12);