Finite Group Databasebeta

← Prev (#49087834) Next (#49087836) →

C2×C17⋊(D7⋊(C52⋊C3)) #49087835

order35700
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C17⋊(D7⋊(C52⋊C3))
unambiguous semidirect product(C2×C17)⋊(D7⋊(C52⋊C3))
unambiguous semidirect product(C2×D119)⋊(C52⋊C3)

Splittings

Fitting, socleC2×C52×C7×C17 ⋊ C2×C3
derived, HallC52×C7×C17 ⋊ C22×C3
HallC2×C52×D119 ⋊ C3
HallC17×C7⋊(C52⋊C3) ⋊ C22
HallC7⋊(C52⋊C3) ⋊ C2×D17
HallC2×D119 ⋊ C52⋊C3
HallC52×C17 ⋊ C2×AGL(1,𝔽7)
HallC52×C7 ⋊ C2×C3×D17
HallC7×C17 ⋊ C22×C52⋊C3
SylowC52 ⋊ C2×C17⋊AGL(1,𝔽7)
SylowC17 ⋊ C2×D7⋊(C52⋊C3)
SylowC7 ⋊ C2×D17×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C17⋊(D7⋊(C52⋊C3))
commutator, cosocle, hypocenterC52×C7×C17C22×C3
FrattiniC1G
Fitting, socleC2×C52×C7×C17C2×C3
LCSG ▷ C52×C7×C17
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3570

Conjugacy classes & character table

1070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 309);