Finite Group Databasebeta

C4×Dic248 #16847571

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

Aliases

direct productC4×Dic248

Splittings

SylowC31 ⋊ C4×Q32

Subgroups

subgroupG/H
centerC2×C4D248
commutatorC8×C31C22×C4
FrattiniC2×C8C22×D31
FittingC4×C16×C31C2
socle, prime radicalC22×C31C2×D8
cosocleC2×C8×C31C23
hypercenterC4×C16D31
hypocenterC31C4×Q32
LCSG ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×C16

150 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, 6370);