Finite Group Databasebeta

← Prev (#44567271) Next (#44567273) →

ΓL(1,𝔽8)×D13×C59 #44567272

order32214
automorphism?
homologyAbelianization (H1) = C2×C3×C59 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D13×C59

Splittings

Fitting, socle, HallC7×C13×C59 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C59
HallC13×ΓL(1,𝔽8)×C59 ⋊ C2
HallC7×D13×C59 ⋊ C3
HallC13×C59 ⋊ C2×ΓL(1,𝔽8)
HallC7×C59 ⋊ C3×D13
HallC13×ΓL(1,𝔽8) ⋊ C2×C59
HallC7×D13 ⋊ C3×C59
SylowC13 ⋊ C2×ΓL(1,𝔽8)×C59
SylowC7 ⋊ C3×D13×C59

Subgroups

subgroupG/H
center, hypercenterC59ΓL(1,𝔽8)×D13
commutator, cosocle, hypocenterC7×C13C2×C3×C59
FrattiniC1G
Fitting, socleC7×C13×C59C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5369

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32214, 26);