Finite Group Databasebeta

#137×Dic31 #16854532

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#137×Dic31

Splittings

SylowC31 ⋊ C4×#137

Subgroups

subgroupG/H
centerC22C2×D4×D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC2×C31×#137C2
socleC22×C31C22×D4
prime radicalC2×#41×C31C22
cosocleC2×C4×C31C24
hypercenterC2×#137D31
hypocenterC31C4×#137
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 13331);