Finite Group Databasebeta

C2×#14543695 #17957979

order4352
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#14543695

Splittings

SylowC17 ⋊ C2×#1311

Subgroups

subgroupG/H
centerC22×C8C2×#595
commutatorC2×C17C2×C82
FrattiniC2×C8C22×#595
FittingC22×C16×C17C4
socle, prime radicalC23×C17C4×C8
cosocleC8×Dic17C23
hypercenterC22×C16#595
hypocenterC17C2×#1311
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C22×C16

366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1093223);