Finite Group Databasebeta

← Prev (#37563084) Next (#37563086) →

D7×C41×AGL(1,𝔽7) #37563085

order24108
automorphism?
homologyAbelianization (H1) = C22×C3×C41 · Schur multiplier (H2) = C2

Aliases

direct productD7×C41×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×D7×C41)
unambiguous semidirect product(C7×AGL(1,𝔽7))⋊(C2×C41)
unambiguous semidirect product(D7×ΓL(1,𝔽8))⋊(C2×C41)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D7)⋊(C2×C41)

Splittings

Fitting, socle, HallC72×C41 ⋊ C22×C3
derived, SylowC72 ⋊ C22×C3×C41
HallD72×C41 ⋊ C3
HallC7×ΓL(1,𝔽8)×C41 ⋊ C22
HallD72 ⋊ C3×C41
HallC7×ΓL(1,𝔽8) ⋊ C22×C41

Subgroups

subgroupG/H
center, hypercenterC41D7×AGL(1,𝔽7)
commutator, cosocle, hypocenterC72C22×C3×C41
FrattiniC1G
Fitting, socleC72×C41C22×C3
LCSG ▷ C72
UCSC1 ◁ C41

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1722

Conjugacy classes & character table

1435 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24108, 92);