Finite Group Databasebeta

C2×#14543704 #17958103

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

Aliases

direct productC2×#14543704

Splittings

SylowC17 ⋊ C2×#1314

Subgroups

subgroupG/H
centerC22×C4C22⋊#595
commutatorC22×C17C22×C16
FrattiniC22×C4C22×#595
FittingC24×C4×C17C4
socleC23×C17C22⋊C8
prime radicalC25×C17C8
cosocleC22×#3622C23
hypercenterC24×C4#595
hypocenterC17C2×#1314
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1093347);