Finite Group Databasebeta

C2×M16×Dic31 #16854118

order3968
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×Dic31

Splittings

SylowC31 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×D31
commutatorC2×C31C22×C42
FrattiniC2×C4C23×D31
FittingC22×M16×C31C2
socleC23×C31C22×C4
prime radicalC24×C31C2×C4
cosocleC2×C4×C31C24
hypercenterC22×M16D31
hypocenterC31C2×C4×M16
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C22×M16

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 12917);