Finite Group Databasebeta

C2×#135×D31 #16860435

order3968
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#135×D31

Splittings

FittingC2×C31×#135 ⋊ C2
SylowC31 ⋊ C22×#135

Subgroups

subgroupG/H
centerC2×C4D4×D31
commutator, cosocleC4×C31C25
FrattiniC4C24×D31
FittingC2×C31×#135C2
socleC22×C31C22×D4
hypercenterC2×#135D31
hypocenterC31C22×#135
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 992

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 19234);