Finite Group Databasebeta

C4×#11758478 #16854131

order3968
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11758478

Splittings

FittingC2×C4×C8×C31 ⋊ C2
SylowC31 ⋊ C4×#131

Subgroups

subgroupG/H
centerC4×C8C2×D31
commutatorC2×C31C22×C42
FrattiniC2×C4C23×D31
FittingC2×C4×C8×C31C2
socleC22×C31C23×C4
prime radicalC2×#92495C22
cosocleC2×C4×C31C24
hypercenterC2×C4×C8D31
hypocenterC31C4×#131
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

1040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 12930);