Finite Group Databasebeta

C2×Dic4024 #44566709

order32192
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic4024

Splittings

SylowC503 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D4024
commutator, cosocleC8×C503C23
FrattiniC8C22×D503
FittingC2×C16×C503C2
socle, prime radicalC22×C503D8
hypercenterC2×C16D503
hypocenterC503C2×Q32
LCSG ▷ C8×C503 ▷ C4×C503 ▷ C2×C503 ▷ C503
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32192

Conjugacy classes & character table

8054 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32192, 977);