Finite Group Databasebeta

← Prev (#36339441) Next (#36339443) →

C32×C7⋊#66776 #36339442

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

Aliases

direct productC32×C7⋊#66776

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C4
derived, HallC5×C7×C17 ⋊ C32×C4
HallC32×C7×C17 ⋊ AGL(1,𝔽5)
HallC32×C5×C17 ⋊ Dic7
HallC32×C5×C7 ⋊ #595
HallC32×C17 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C17 ⋊ C32×AGL(1,𝔽5)
HallC5×C17 ⋊ C32×Dic7
HallC32×C7 ⋊ #66776
HallC32×C5 ⋊ C7⋊#595
HallC5×C7 ⋊ C32×#595
SylowC17 ⋊ C32×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C32×#66776
SylowC5 ⋊ C32×C7⋊#595

Subgroups

subgroupG/H
center, hypercenterC32C7⋊#66776
commutator, hypocenterC5×C7×C17C32×C4
FrattiniC1G
Fitting, socleC32×C5×C7×C17C4
prime radicalC32×C7×D85C2
cosocleC7×D85C2×C32
LCSG ▷ C5×C7×C17
UCSC1 ◁ C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

1413 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 274);