Finite Group Databasebeta

← Prev (#38788954) Next (#38788956) →

C3×C5×ΓL(1,𝔽8)×D41 #38788955

order25830
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×ΓL(1,𝔽8)×D41
unambiguous semidirect product(C5×C7×D41)⋊C32
unambiguous semidirect product(C3×C5×C7×D41)⋊C3

Splittings

Fitting, socleC3×C5×C7×C41 ⋊ C2×C3
derived, HallC7×C41 ⋊ C2×C32×C5
HallC3×C5×ΓL(1,𝔽8)×C41 ⋊ C2
HallC5×C7×D41 ⋊ C32
HallC3×ΓL(1,𝔽8)×C41 ⋊ C2×C5
HallC5×C7×C41 ⋊ C2×C32
HallC7×D41 ⋊ C32×C5
HallC5×C41 ⋊ C2×C3×ΓL(1,𝔽8)
SylowC41 ⋊ C2×C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C32×D41
SylowC7 ⋊ C32×C5×D41

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)×D41
commutator, cosocle, hypocenterC7×C41C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C41C2×C3
LCSG ▷ C7×C41
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4305

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 59);