Finite Group Databasebeta

C2×D17⋊#368 #17978439

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

Aliases

direct productC2×D17⋊#368
unambiguous semidirect productD17⋊(C2×#368)

Splittings

SylowC17 ⋊ C22×#368

Subgroups

subgroupG/H
centerC2×C4#10587534
commutatorC8×C17C23×C4
FrattiniC8C23×#595
FittingC22×C16×C17C4
socleC22×C17C2×#107
prime radicalC23×D17Q16
cosocleC8×D17C24
hypercenterC22×C16#595
hypocenterC17C22×#368
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

344 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113683);