Finite Group Databasebeta

C2×#14544762 #17969862

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14544762

Splittings

SylowC17 ⋊ C2×#1870

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC22×C22⋊C4×C17C4
socleC24×C17C22×C4
prime radicalC23×C22⋊D17C4
cosocleC22×Dic17C24
hypercenterC22×C22⋊C4#595
hypocenterC17C2×#1870
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C22⋊C4

2286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1105106);