Finite Group Databasebeta

C2×#14531930 #17196909

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14531930

Splittings

FittingC2×C17×#388 ⋊ C2
SylowC17 ⋊ C2×#2376

Subgroups

subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#388C2
socleC24×C17C24
prime radicalC23×C22⋊D17C22
cosocleC23×C17C25
hypercenterC2×#388D17
hypocenterC17C2×#2376
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

2870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 332153);