Finite Group Databasebeta

C2×#31775948 #46855428

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

Aliases

direct productC2×#31775948

Splittings

SylowC547 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#22576761
commutator, cosocleC8×C547C23
FrattiniC8C22×D547
FittingC2×Q16×C547C2
socle, prime radicalC22×C547D8
hypercenterC2×Q16D547
hypocenterC547C2×Q32
LCSG ▷ C8×C547 ▷ C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35008

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, 976);