Finite Group Databasebeta

C4×Dic2186 #46854073

order34976
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic2186

Splittings

SylowC1093 ⋊ C4×Q8

Subgroups

subgroupG/H
centerC2×C4C2×D1093
commutatorC2×C1093C22×C4
FrattiniC22C22×D1093
FittingC42×C1093C2
socle, prime radical, cosocleC22×C1093C23
hypercenterC42D1093
hypocenterC1093C4×Q8
LCSG ▷ C2×C1093 ▷ C1093
UCSC1 ◁ C2×C4 ◁ C42

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34976

Conjugacy classes & character table

8756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34976, 112);