Finite Group Databasebeta

C2×#14545123 #17978413

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14545123

Splittings

SylowC17 ⋊ C22×#364

Subgroups

subgroupG/H
centerC2×C8C4⋊#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
FittingC2×C4×C8×C17C4
socleC22×C17C2×C4⋊C8
prime radicalC23×D17M16
cosocleC2×#3622C24
hypercenterC2×C4×C8#595
hypocenterC17C22×#364
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113657);