Finite Group Databasebeta

C2×#30630272 #44543085

order31936
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#30630272

Splittings

SylowC499 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23C22⋊D499
commutatorC4×C499C22×C4
FrattiniC2×C4C22×D499
Fitting, prime radicalC22×D4×C499C2
socleC23×C499D4
cosocleC2×C4×C499C23
hypercenterC22×D4D499
hypocenterC499C2×#102
LCSG ▷ C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15968

Conjugacy classes & character table

5008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 536);