Finite Group Databasebeta

C4×#22547795 #44543051

order31936
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#22547795

Splittings

SylowC499 ⋊ C4×M16

Subgroups

subgroupG/H
centerC42C2×D499
commutatorC2×C499C2×C42
FrattiniC2×C4C22×D499
FittingC2×C42×C499C2
socleC22×C499C22×C4
prime radicalC23×C499C2×C4
cosocleC2×C4×C499C23
hypercenterC2×C42D499
hypocenterC499C4×M16
LCSG ▷ C2×C499 ▷ C499
UCSC1 ◁ C42 ◁ C2×C42

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15968

Conjugacy classes & character table

8008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 502);