Finite Group Databasebeta

C2×#14545347 #17979413

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#14545347

Splittings

FittingC22×M16×C17 ⋊ C4
SylowC17 ⋊ C2×#2873

Subgroups

subgroupG/H
centerC2×C4C23×#595
commutatorC2×C17C23×C42
FrattiniC4C24×#595
FittingC22×M16×C17C4
socleC22×C17C22×C42
prime radicalC24×D17C2×C4
cosocleC4×D17C25
hypercenterC22×M16#595
hypocenterC17C2×#2873
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×M16

3342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114657);