Finite Group Databasebeta

C2×#14531167 #17192595

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×#14531167

Splittings

SylowC17 ⋊ C2×#2280

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC25×C4×C17C2
socleC24×C17C24
prime radicalC26×C17C22
cosocleC23×C17C25
hypercenterC25×C4D17
hypocenterC17C2×#2280
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C25×C4

7630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327839);