Finite Group Databasebeta

C2×#14521118 #16854388

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

Aliases

direct productC2×#14521118

Splittings

FittingC22×M16×C31 ⋊ C2
SylowC31 ⋊ C2×#435

Subgroups

subgroupG/H
centerC22×C4C22×D31
commutatorC22×C31C23×C4
FrattiniC2×C4C23×D31
FittingC22×M16×C31C2
socleC23×C31C22×C4
prime radicalC22×C22⋊D31C4
cosocleC2×C4×C31C24
hypercenterC22×M16D31
hypocenterC31C2×#435
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C22×M16

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 13187);