Finite Group Databasebeta

C2×#14520875 #16847488

order3968
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14520875

Splittings

SylowC31 ⋊ C2×#366

Subgroups

subgroupG/H
centerC23D248
commutatorC8×C31C22×C4
FrattiniC2×C8C22×D31
FittingC22×C16×C31C2
socle, prime radicalC23×C31D8
cosocleC2×C8×C31C23
hypercenterC22×C16D31
hypocenterC31C2×#366
LCSG ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3968

Conjugacy classes & character table

1004 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 6287);