Finite Group Databasebeta

← Prev (#38760849) Next (#38760851) →

C7×(C241⋊C3)⋊C5 #38760850

order25305
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×(C241⋊C3)⋊C5
unambiguous semidirect product(C241⋊C3)⋊(C5×C7)
unambiguous semidirect product(C241⋊C5)⋊(C3×C7)
unambiguous semidirect product(C7×C241⋊C3)⋊C5

Splittings

Fitting, socle, HallC7×C241 ⋊ C3×C5
derived, SylowC241 ⋊ C3×C5×C7
HallC7×C241⋊C5 ⋊ C3
HallC7×C241⋊C3 ⋊ C5
HallC241⋊C5 ⋊ C3×C7
HallC241⋊C3 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC7(C241⋊C3)⋊C5
commutator, cosocle, hypocenterC241C3×C5×C7
FrattiniC1G
Fitting, socleC7×C241C3×C5
LCSG ▷ C241
UCSC1 ◁ C7

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1687

Conjugacy classes & character table

217 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25305, 7);