Finite Group Databasebeta

C2×#14544414 #17966713

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14544414

Splittings

SylowC17 ⋊ C2×#1588

Subgroups

subgroupG/H
centerC23D4×#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×#102C4
socleC23×C17C4×D4
prime radicalC22×D4×C17C2×C4
cosocleC4×Dic17C24
hypercenterC2×#102#595
hypocenterC17C2×#1588
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1101957);