Finite Group Databasebeta

C2×#14521065 #16854252

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14521065

Splittings

FittingC22×M16×C31 ⋊ C2
SylowC31 ⋊ C2×#421

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC22×M16×C31C2
socleC22×C31C2×C22⋊C4
prime radicalC22×#92495C2
cosocleC2×C4×C31C24
hypercenterC22×M16D31
hypocenterC31C2×#421
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 992

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 13051);