Finite Group Databasebeta

C2×#14543668 #17951301

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14543668

Splittings

SylowC17 ⋊ C2×#1299

Subgroups

subgroupG/H
centerC22×C4C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC22×M16×C17C4
socleC23×C17#95
prime radicalC24×C17C4⋊C4
cosocleC2×C4×Dic17C23
hypercenterC22×M16#595
hypocenterC17C2×#1299
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1086545);