Finite Group Databasebeta

C2×#14545896 #17982834

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14545896

Splittings

FittingC23×C4×C17 ⋊ C8
SylowC17 ⋊ C2×#1458

Subgroups

subgroupG/H
centerC2×C4C22⋊#3633
commutatorC22×C17C23×C8
FrattiniC22C23×#3633
FittingC23×C4×C17C8
socleC22×C17C2×C22⋊C8
prime radicalC24×D17C2×C4
cosocleC22×#595C24
hypercenterC23×C4#3633
hypocenterC17C2×#1458
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 1118078);