Finite Group Databasebeta

C2×#14544593 #17968580

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14544593

Splittings

FittingC2×C17×#108 ⋊ C4
SylowC17 ⋊ C2×#1773

Subgroups

subgroupG/H
centerC2×C4D4×#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC2×C17×#108C4
socleC22×C17C4×C4⋊C4
prime radicalC23×D17#41
cosocleC2×C4×D17C24
hypercenterC2×#108#595
hypocenterC17C2×#1773
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#108

1062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 1103824);