Finite Group Databasebeta

← Prev (#49087551) Next (#49087553) →

C25×ΓL(1,𝔽8)⋊#595 #49087552

order35700
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×ΓL(1,𝔽8)⋊#595
unambiguous semidirect productΓL(1,𝔽8)⋊(C25×#595)
unambiguous semidirect product(C7⋊#595)⋊(C3×C25)
unambiguous semidirect product(C25×C7⋊#595)⋊C3

Splittings

Fitting, HallC7×C17×C25 ⋊ C3×C4
derived, HallC7×C17 ⋊ C3×C4×C25
HallC25×C7⋊#595 ⋊ C3
HallC17×ΓL(1,𝔽8)×C25 ⋊ C4
HallΓL(1,𝔽8)×C25 ⋊ #595
HallC7⋊#595 ⋊ C3×C25
HallC17×C25 ⋊ ΓL(1,𝔽8)⋊C4
HallC17×ΓL(1,𝔽8) ⋊ C4×C25
HallC7×C25 ⋊ C3×#595
HallΓL(1,𝔽8) ⋊ C25×#595
SylowC17 ⋊ C25×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C25×#595

Subgroups

subgroupG/H
center, hypercenterC25ΓL(1,𝔽8)⋊#595
commutator, hypocenterC7×C17C3×C4×C25
FrattiniC5C5×ΓL(1,𝔽8)⋊#595
FittingC7×C17×C25C3×C4
socleC5×C7×C17C3×C4×C5
prime radicalC5×ΓL(1,𝔽8)×D17C2×C5
cosocleC5×C7×D17C2×C3×C5
LCSG ▷ C7×C17
UCSC1 ◁ C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2975

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 26);