Finite Group Databasebeta

← Prev (#40998704) Next (#40998706) →

C5×ΓL(1,𝔽8)⋊D127 #40998705

order26670
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)⋊D127
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D127)

Splittings

Fitting, socle, HallC5×C7×C127 ⋊ C2×C3
derived, HallC7×C127 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C127 ⋊ C2
HallC5×D889 ⋊ C3
HallΓL(1,𝔽8)×C127 ⋊ C2×C5
HallD889 ⋊ C3×C5
HallC5×C127 ⋊ AGL(1,𝔽7)
SylowC127 ⋊ C5×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ D127
HallC5×C7 ⋊ C3×D127
HallΓL(1,𝔽8) ⋊ C5×D127
SylowC7 ⋊ C3×C5×D127

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)⋊D127
commutator, cosocle, hypocenterC7×C127C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C127C2×C3
LCSG ▷ C7×C127
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4445

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26670, 39);