Finite Group Databasebeta

← Prev (#17969220) Next (#17969222) →

C2×#14544630 #17969221

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14544630
unambiguous semidirect productD17⋊#1792

Splittings

FittingC2×C17×H(5,𝔽2) ⋊ C4
SylowC17 ⋊ C2×#1792

Subgroups

subgroupG/H
centerC22#11763750
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×H(5,𝔽2)C4
socleC22×C17#379
prime radicalC2×H(5,𝔽2)×D17C2
cosocleC2×C4×D17C24
hypercenterC2×H(5,𝔽2)#595
hypocenterC17C2×#1792
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×H(5,𝔽2)

4114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1104465);