Finite Group Databasebeta

C2×#14545125 #17978415

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14545125

Splittings

SylowC17 ⋊ C2×#2153

Subgroups

subgroupG/H
centerC2×C4C2×C4⋊#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
FittingC22×M16×C17C4
socleC22×C17C2×C4⋊C8
prime radicalC24×C17M16
cosocleC2×#3622C24
hypercenterC22×M16#595
hypocenterC17C2×#2153
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1113659);