Finite Group Databasebeta

C2×#30630295 #44543522

order31936
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30630295

Splittings

SylowC499 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#22547796
commutator, cosocleC8×C499C23
FrattiniC8C22×D499
Fitting, prime radicalC2×D8×C499C2
socleC22×C499D8
hypercenterC2×D8D499
hypocenterC499C2×SD32
LCSG ▷ C8×C499 ▷ C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15968

Conjugacy classes & character table

3508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 973);