Finite Group Databasebeta

C2×#14528884 #17034152

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14528884

Splittings

SylowC17 ⋊ C2×#1826

Subgroups

subgroupG/H
centerC22×C4C2×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C4×C22⋊C4×C17C2
socleC23×C17C2×C22⋊C4
prime radicalC25×C17D4
cosocleC22×C4×C17C24
hypercenterC2×C4×C22⋊C4D17
hypocenterC17C2×#1826
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 169396);