Finite Group Databasebeta

C2×#30630274 #44543088

order31936
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#30630274

Splittings

SylowC499 ⋊ C2×#103

Subgroups

subgroupG/H
centerC23C22⋊D499
commutatorC4×C499C22×C4
FrattiniC2×C4C22×D499
FittingC2×C4⋊C4×C499C2
socle, prime radicalC23×C499D4
cosocleC2×C4×C499C23
hypercenterC2×C4⋊C4D499
hypocenterC499C2×#103
LCSG ▷ C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31936

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, 539);