Finite Group Databasebeta

C2×#31775994 #46855523

order35008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#31775994

Splittings

SylowC547 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D547
commutator, cosocleC22×C547C24
FrattiniC22C23×D547
FittingC2×C42×C547C2
socle, prime radicalC23×C547C23
hypercenterC2×C42D547
hypocenterC547C2×#125
LCSG ▷ C22×C547 ▷ C547
UCSC1 ◁ C23 ◁ C2×C42

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35008

Conjugacy classes & character table

8764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35008, 1071);