Finite Group Databasebeta

C2×#14527607 #17003722

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14527607

Splittings

FittingC2×C17×#334 ⋊ C2
SylowC17 ⋊ C2×#1580

Subgroups

subgroupG/H
centerC22×C4D4×D17
commutatorC4×C17C23×C8
FrattiniC42C23×D17
FittingC2×C17×#334C2
socleC23×C17C4×D4
prime radicalC22×D136C4
cosocleC42×C17C24
hypercenterC2×#334D17
hypocenterC17C2×#1580
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 138966);