Finite Group Databasebeta

C2×#14526908 #16949290

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14526908

Splittings

SylowC17 ⋊ C2×#1393

Subgroups

subgroupG/H
centerC23#10587477
commutatorC2×C4×C17C2×C42
FrattiniC22×D4C22×D17
FittingC22×C17×#99C2
socleC23×C17#99
prime radicalC23×D4×C17C22
cosocleC22×D4×C17C23
hypercenterC22×#99D17
hypocenterC17C2×#1393
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24 ◁ C23×D4 ◁ C22×#99

1154 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, 84534);