Finite Group Databasebeta

C2×#14544512 #17968282

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14544512

Splittings

FittingC2×C17×C22⋊C8 ⋊ C4
SylowC17 ⋊ C2×#1749

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC22×C17C22×C42
FrattiniC2×C4C23×#595
FittingC2×C17×C22⋊C8C4
socleC23×C17C2×C42
prime radicalC24×D17C2×C4
cosocleC2×C4×D17C24
hypercenterC2×C22⋊C8#595
hypocenterC17C2×#1749
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

2286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103526);