Finite Group Databasebeta

C2×#14544013 #17964200

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14544013

Splittings

SylowC17 ⋊ C22×#324

Subgroups

subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C17C23×C8
FrattiniC23C23×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17C2×C4
cosocleC22×Dic17C24
hypercenterC22×C4⋊C4#595
hypocenterC17C22×#324
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

1806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1099444);