Finite Group Databasebeta

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C29×D651 #49179971

order37758
automorphism?
homologyAbelianization (H1) = C2×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×D651
unambiguous semidirect productC3⋊(C29×D217)
unambiguous semidirect productC7⋊(C29×D93)
unambiguous semidirect productC31⋊(C29×D21)

Splittings

Fitting, socle, HallC3×C7×C29×C31 ⋊ C2
derived, HallC3×C7×C31 ⋊ C2×C29
HallC7×C29×C31 ⋊ D3
HallC3×C29×C31 ⋊ D7
HallC29×C31 ⋊ D21
HallC3×C7×C29 ⋊ D31
HallC7×C31 ⋊ D3×C29
HallC7×C29 ⋊ D93
HallC3×C31 ⋊ D7×C29
HallC3×C29 ⋊ D217
SylowC31 ⋊ C29×D21
HallC3×C7 ⋊ C29×D31
SylowC7 ⋊ C29×D93
SylowC3 ⋊ C29×D217

Subgroups

subgroupG/H
center, hypercenterC29D651
commutator, cosocle, hypocenterC3×C7×C31C2×C29
FrattiniC1G
Fitting, socleC3×C7×C29×C31C2
LCSG ▷ C3×C7×C31
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18879

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(37758, 20);