Finite Group Databasebeta

C2×#14529399 #17036610

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14529399

Splittings

SylowC17 ⋊ C2×#1924

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC23×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C4×C22⋊C4×C17C2
socleC24×C17C22×C4
prime radicalC25×C17C2×C4
cosocleC22×C4×C17C24
hypercenterC2×C4×C22⋊C4D17
hypocenterC17C2×#1924
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 171854);