Finite Group Databasebeta

C2×#14543901 #17962581

order4352
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14543901

Splittings

SylowC17 ⋊ C2×#1401

Subgroups

subgroupG/H
centerC2×C8C22⋊#595
commutatorC4×C17C22×C16
FrattiniC2×C8C22×#595
FittingC2×C17×#131C4
socleC22×C17C22⋊C16
prime radicalC2×#41×C17C8
cosocleC2×#63214C23
hypercenterC2×#131#595
hypocenterC17C2×#1401
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1097825);