Finite Group Databasebeta

C2×#14526723 #16943454

order4352
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14526723

Splittings

SylowC17 ⋊ C2×#1322

Subgroups

subgroupG/H
centerC22×C4#63227
commutatorC22×C17C22×C16
FrattiniC22×C8C22×D17
FittingC2×C17×C22⋊C16C2
socleC23×C17C22⋊C8
prime radicalC24×C17C2×C8
cosocleC22×C8×C17C23
hypercenterC2×C22⋊C16D17
hypocenterC17C2×#1322
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C2×C22⋊C16

466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 78698);