Finite Group Databasebeta

C2×#14545989 #17983096

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#14545989

Splittings

SylowC17 ⋊ C2×#2164

Subgroups

subgroupG/H
centerC23C22×#3633
commutatorC22×C17C23×C8
FrattiniC22C23×#3633
FittingC2×C22⋊C4×C17C8
socleC23×C17C22×C8
prime radicalC24×C17C2×C8
cosocleC2×#3624C24
hypercenterC2×C22⋊C4#3633
hypocenterC17C2×#2164
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C22⋊C4

610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118340);