Finite Group Databasebeta

C2×#14545951 #17983026

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14545951

Splittings

SylowC17 ⋊ C2×#2112

Subgroups

subgroupG/H
centerC23C22×#3633
commutatorC22×C17C23×C8
FrattiniC22C23×#3633
Fitting, prime radicalC25×C17C8
socleC23×C17C22×C8
cosocleC2×#3624C24
hypercenterC25#3633
hypocenterC17C2×#2112
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25

1406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118270);