Finite Group Databasebeta

C2×#14545863 #17982403

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

Aliases

direct productC2×#14545863

Splittings

SylowC17 ⋊ C2×#1378

Subgroups

subgroupG/H
centerC22(C2×#3633)⋊C4
commutatorC22×C17C2×C4×C8
FrattiniC2×C4C22×#3633
FittingC2×M16×C17C8
socleC22×C17#336
prime radicalC23×D17C2×C8
cosocleC2×#63242C23
hypercenterC2×M16#3633
hypocenterC17C2×#1378
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1117647);