Finite Group Databasebeta

C2×#14520811 #16845424

order3968
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14520811

Splittings

SylowC31 ⋊ C2×#340

Subgroups

subgroupG/H
centerC24C22⋊D31
commutatorC4×C31C2×C42
FrattiniC22×C4C22×D31
FittingC22×C4⋊C4×C31C2
socle, prime radicalC24×C31D4
cosocleC22×C4×C31C23
hypercenterC22×C4⋊C4D31
hypocenterC31C2×#340
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3968

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, 4223);