Finite Group Databasebeta

C2×#14544377 #17966600

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14544377

Splittings

SylowC17 ⋊ C2×#1579

Subgroups

subgroupG/H
centerC23D4×#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
FittingC22×Q16×C17C4
socle, prime radicalC23×C17C4×D4
cosocleC4×Dic17C24
hypercenterC22×Q16#595
hypocenterC17C2×#1579
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1101844);