Finite Group Databasebeta

C4×#11758475 #16848264

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC4×#11758475

Splittings

FittingC4×C4⋊C4×C31 ⋊ C2
SylowC31 ⋊ C4×#126

Subgroups

subgroupG/H
centerC22×C4C22×D31
commutatorC22×C31C23×C4
FrattiniC23C23×D31
FittingC4×C4⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC23×D31C23
hypercenterC4×C4⋊C4D31
hypocenterC31C4×#126
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

516 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, 7063);