Finite Group Databasebeta

C2×#14530811 #17188494

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

Aliases

direct productC2×#14530811

Splittings

FittingC2×C17×#355 ⋊ C2
SylowC17 ⋊ C2×#2204

Subgroups

subgroupG/H
centerC22#11762997
commutator, cosocleC2×Q8×C17C24
FrattiniC2×Q8C23×D17
FittingC2×C17×#355C2
socleC22×C17B(4,𝔽2)
hypercenterC2×#355D17
hypocenterC17C2×#2204
LCSG ▷ C2×Q8×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 323738);