Finite Group Databasebeta

C2×#31799925 #47986388

order35456
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#31799925

Splittings

SylowC277 ⋊ C2×#396

Subgroups

subgroupG/H
centerC24C22×D277
commutator, cosocleC23×C277C24
FrattiniC23C23×D277
FittingC22×C22⋊C4×C277C2
socleC24×C277C23
prime radicalC25×C277C22
hypercenterC22×C22⋊C4D277
hypocenterC277C2×#396
LCSG ▷ C23×C277 ▷ C277
UCSC1 ◁ C24 ◁ C22×C22⋊C4

908 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17728

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, 7731);