Finite Group Databasebeta

C2×#14544637 #17969238

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14544637

Splittings

FittingC22×#41×C17 ⋊ C4
SylowC17 ⋊ C2×#1796

Subgroups

subgroupG/H
centerC22#11763750
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC22×#41×C17C4
socleC22×C17#379
prime radicalC22×#10587697C2
cosocleC2×C4×D17C24
hypercenterC22×#41#595
hypocenterC17C2×#1796
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41

3602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

218 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1104482);