Finite Group Databasebeta

C2×#31799943 #47986421

order35456
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#31799943

Splittings

SylowC277 ⋊ C2×#400

Subgroups

subgroupG/H
centerC24C22×D277
commutator, cosocleC23×C277C24
FrattiniC23C23×D277
FittingC2×#95×C277C2
socle, prime radicalC24×C277C23
hypercenterC2×#95D277
hypocenterC277C2×#400
LCSG ▷ C23×C277 ▷ C277
UCSC1 ◁ C24 ◁ C2×#95

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35456

Conjugacy classes & character table

5564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35456, 7764);