Finite Group Databasebeta

← Prev (#36339436) Next (#36339438) →

C32×C7×#66775 #36339437

order21420
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×#66775

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C4
derived, HallC5×C17 ⋊ C32×C4×C7
HallC32×C7×C17 ⋊ AGL(1,𝔽5)
HallC32×C5×C17 ⋊ C4×C7
HallC5×C7×C17 ⋊ C32×C4
HallC32×C5×C7 ⋊ #595
HallC32×C17 ⋊ C7×AGL(1,𝔽5)
HallC7×C17 ⋊ C32×AGL(1,𝔽5)
HallC32×C5 ⋊ C7×#595
HallC5×C7 ⋊ C32×#595
SylowC17 ⋊ C32×C7×AGL(1,𝔽5)
SylowC5 ⋊ C32×C7×#595

Subgroups

subgroupG/H
center, hypercenterC32×C7#66775
commutator, hypocenterC5×C17C32×C4×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C17C4
prime radicalC32×C7×D85C2
cosocleD85C2×C32×C7
LCSG ▷ C5×C17
UCSC1 ◁ C32×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

1575 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 269);