Finite Group Databasebeta

C2×#14544087 #17964701

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14544087

Splittings

SylowC17 ⋊ C2×#1479

Subgroups

subgroupG/H
centerC23C2×C22⋊#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
FittingC2×C4×Q8×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC4×Dic17C24
hypercenterC2×C4×Q8#595
hypocenterC17C2×#1479
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

1282 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, 1099945);