Finite Group Databasebeta

C2×#14526846 #16945689

order4352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14526846

Splittings

SylowC17 ⋊ C2×#1366

Subgroups

subgroupG/H
centerC22#11762557
commutatorC42×C17C22×C4
FrattiniC4×C8C22×D17
FittingC2×C17×#364C2
socleC22×C17#333
prime radicalC23×C17#100
cosocleC4×C8×C17C23
hypercenterC2×#364D17
hypocenterC17C2×#1366
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#364

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 80933);