Finite Group Databasebeta

C2×#31775946 #46855425

order35008
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#31775946

Splittings

SylowC547 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#22576761
commutator, cosocleC8×C547C23
FrattiniC8C22×D547
Fitting, prime radicalC2×D8×C547C2
socleC22×C547D8
hypercenterC2×D8D547
hypocenterC547C2×SD32
LCSG ▷ C8×C547 ▷ C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17504

Conjugacy classes & character table

3844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35008, 973);