Finite Group Databasebeta

← Prev (#36339575) Next (#36339577) →

C2×C32×C17×D35 #36339576

order21420
automorphism?
homologyAbelianization (H1) = C22×C32×C17 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C17×D35
unambiguous semidirect product(C2×C5)⋊(C32×D7×C17)

Splittings

Fitting, socleC2×C32×C5×C7×C17 ⋊ C2
derived, HallC5×C7 ⋊ C22×C32×C17
HallC32×C5×C7×C17 ⋊ C22
HallC32×C7×C17 ⋊ C2×D5
HallC32×C5×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C22×C32
HallC32×C5×C7 ⋊ C22×C17
HallC7×C17 ⋊ C2×C32×D5
HallC5×C17 ⋊ C2×C32×D7
HallC32×C7 ⋊ C2×D5×C17
HallC32×C5 ⋊ C2×D7×C17
SylowC7 ⋊ C2×C32×D5×C17
SylowC5 ⋊ C2×C32×D7×C17

Subgroups

subgroupG/H
center, hypercenterC2×C32×C17D35
commutator, cosocle, hypocenterC5×C7C22×C32×C17
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C17C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C32×C17

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10710

Conjugacy classes & character table

5814 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 408);