Finite Group Databasebeta

C2×#14526664 #16924309

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14526664

Splittings

SylowC17 ⋊ C2×#1294

Subgroups

subgroupG/H
centerC24#63227
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC22×C17×C22⋊C8C2
socleC24×C17C22⋊C4
prime radicalC25×C17D4
cosocleC23×C4×C17C23
hypercenterC22×C22⋊C8D17
hypocenterC17C2×#1294
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

1454 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, 59553);