Finite Group Databasebeta

C2×#14545865 #17982407

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14545865

Splittings

SylowC17 ⋊ C2×#1379

Subgroups

subgroupG/H
centerC2×C4C22⋊#3633
commutatorC4×C17C2×C4×C8
FrattiniC2×C4C22×#3633
FittingC2×M16×C17C8
socleC22×C17#336
prime radicalC23×D17M16
cosocleC2×#63242C23
hypercenterC2×M16#3633
hypocenterC17C2×#1379
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1117651);