Finite Group Databasebeta

C2×#14543662 #17951209

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14543662

Splittings

SylowC17 ⋊ C2×#1296

Subgroups

subgroupG/H
centerC24C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socle, prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17C2×#1296
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1086453);