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C29×#13049959 #49179995

order37758
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×#13049959

Splittings

Fitting, socle, HallC7×C29×C31 ⋊ C2×C3
derived, HallC7×C31 ⋊ C2×C3×C29
HallC29×#10620253 ⋊ C2
HallD7×C29×C31 ⋊ C3
HallC29×C31 ⋊ AGL(1,𝔽7)
Hall#10620253 ⋊ C2×C29
HallD7×C31 ⋊ C3×C29
HallD7×C29 ⋊ C31⋊C3
HallC7×C29 ⋊ C2×C31⋊C3
SylowC31 ⋊ C29×AGL(1,𝔽7)
HallD7 ⋊ C29×C31⋊C3
SylowC7 ⋊ C2×C29×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC29#13049959
commutator, cosocle, hypocenterC7×C31C2×C3×C29
FrattiniC1G
Fitting, socleC7×C29×C31C2×C3
LCSG ▷ C7×C31
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6293

Conjugacy classes & character table

1653 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37758, 44);