Finite Group Databasebeta

C2×#14544346 #17966342

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14544346

Splittings

SylowC17 ⋊ C2×#1568

Subgroups

subgroupG/H
centerC23C2×C4⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC23×C8×C17C4
socleC23×C17C2×C4⋊C4
prime radicalC24×C17C4⋊C4
cosocleC4×Dic17C24
hypercenterC23×C8#595
hypocenterC17C2×#1568
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1101586);