Finite Group Databasebeta

C2×#14544697 #17969436

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14544697

Splittings

SylowC17 ⋊ C2×#1829

Subgroups

subgroupG/H
centerC22#11763752
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC22×C22⋊C4×C17C4
socleC22×C17#381
prime radicalC23×C22⋊D17C22
cosocleC22×Dic17C24
hypercenterC22×C22⋊C4#595
hypocenterC17C2×#1829
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4

1434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

218 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1104680);