Finite Group Databasebeta

C2×#41×Dic31 #16858893

order3968
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#41×Dic31

Splittings

SylowC31 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC22×C4C22×D31
commutatorC2×C31C24×C4
FrattiniC22C24×D31
Fitting, prime radicalC22×#41×C31C2
socleC23×C31C24
cosocleC22×C31C25
hypercenterC22×#41D31
hypocenterC31C2×C4×#41
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C22×#41

1728 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, 17692);