Finite Group Databasebeta

M16×Dic499 #44543049

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

Aliases

direct productM16×Dic499

Splittings

SylowC499 ⋊ C4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D499
commutatorC2×C499C2×C42
FittingC2×M16×C499C2
socleC22×C499C22×C4
prime radicalC23×C499C2×C4
cosocleC2×C4×C499C23
hypercenterC2×M16D499
hypocenterC499C4×M16
LCSG ▷ C2×C499 ▷ C499
UCSC1 ◁ C2×C4 ◁ C2×M16

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15968

Conjugacy classes & character table

5020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 500);