Finite Group Databasebeta

C2×#14530808 #17188491

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14530808

Splittings

FittingC2×C17×#454 ⋊ C2
SylowC17 ⋊ C2×#2204

Subgroups

subgroupG/H
centerC22#11762995
commutator, cosocleC2×Q8×C17C24
FrattiniC2×Q8C23×D17
FittingC2×C17×#454C2
socleC22×C17B(4,𝔽2)
hypercenterC2×#454D17
hypocenterC17C2×#2204
LCSG ▷ C2×Q8×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#454

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 323735);