Finite Group Databasebeta

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C3×C29×D215 #49153452

order37410
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×C29×D215
unambiguous semidirect productC5⋊(C3×C29×D43)

Splittings

Fitting, socle, HallC3×C5×C29×C43 ⋊ C2
derived, HallC5×C43 ⋊ C2×C3×C29
HallC5×C29×C43 ⋊ C2×C3
HallC3×C29×C43 ⋊ D5
HallC29×C43 ⋊ C3×D5
HallC3×C5×C43 ⋊ C2×C29
HallC3×C5×C29 ⋊ D43
HallC5×C29 ⋊ C3×D43
HallC3×C43 ⋊ D5×C29
SylowC43 ⋊ C3×D5×C29
HallC3×C5 ⋊ C29×D43
SylowC5 ⋊ C3×C29×D43

Subgroups

subgroupG/H
center, hypercenterC3×C29D215
commutator, cosocle, hypocenterC5×C43C2×C3×C29
FrattiniC1G
Fitting, socleC3×C5×C29×C43C2
LCSG ▷ C5×C43
UCSC1 ◁ C3×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18705

Conjugacy classes & character table

9483 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37410, 7);