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C29×#13049955 #49179983

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

Aliases

direct productC29×#13049955

Splittings

Fitting, socle, HallC7×C29×C31 ⋊ C2×C3
derived, HallC7×C31 ⋊ C2×C3×C29
HallC29×#10620253 ⋊ C2
HallC7×C29×D31 ⋊ C3
HallC29×D31 ⋊ ΓL(1,𝔽8)
HallC29×C31 ⋊ C2×ΓL(1,𝔽8)
Hall#10620253 ⋊ C2×C29
HallC7×D31 ⋊ C3×C29
HallC7×C29 ⋊ D31⋊C3
HallD31 ⋊ ΓL(1,𝔽8)×C29
SylowC31 ⋊ C2×ΓL(1,𝔽8)×C29
SylowC7 ⋊ C29×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC29#13049955
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

1305 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37758, 32);