Finite Group Databasebeta

C2×#14526721 #16943448

order4352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14526721

Splittings

FittingC2×C17×#349 ⋊ C2
SylowC17 ⋊ C2×#1321

Subgroups

subgroupG/H
centerC2×C4#10587477
commutatorC2×C4×C17C22×C8
FrattiniC2×M16C22×D17
FittingC2×C17×#349C2
socleC22×C17#323
prime radicalC22×#63252C4
cosocleC2×M16×C17C23
hypercenterC2×#349D17
hypocenterC17C2×#1321
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 78692);