Finite Group Databasebeta

C22×(C22⋊D31)⋊C4 #16858879

order3968
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×(C22⋊D31)⋊C4

Splittings

FittingC22×C22⋊C4×C31 ⋊ C2
SylowC31 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC24C22×D31
commutatorC2×C31C24×C4
FrattiniC22C24×D31
FittingC22×C22⋊C4×C31C2
socleC24×C31C23
prime radicalC23×C22⋊D31C2
cosocleC22×C31C25
hypercenterC22×C22⋊C4D31
hypocenterC31C22×C4×D4
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C24 ◁ C22×C22⋊C4

2528 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, 17678);