Finite Group Databasebeta

← Prev (#44443300) Next (#44443302) →

C19×ΓL(1,𝔽8)×D37 #44443301

order29526
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×ΓL(1,𝔽8)×D37

Splittings

Fitting, socle, HallC7×C19×C37 ⋊ C2×C3
derived, HallC7×C37 ⋊ C2×C3×C19
HallC19×ΓL(1,𝔽8)×C37 ⋊ C2
HallC7×C19×D37 ⋊ C3
HallΓL(1,𝔽8)×C37 ⋊ C2×C19
HallC19×C37 ⋊ C2×ΓL(1,𝔽8)
HallC7×D37 ⋊ C3×C19
HallC7×C19 ⋊ C3×D37
SylowC37 ⋊ C2×C19×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C19×D37

Subgroups

subgroupG/H
center, hypercenterC19ΓL(1,𝔽8)×D37
commutator, cosocle, hypocenterC7×C37C2×C3×C19
FrattiniC1G
Fitting, socleC7×C19×C37C2×C3
LCSG ▷ C7×C37
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4921

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29526, 34);