Finite Group Databasebeta

D4×Dic1063 #46801158

order34016
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD4×Dic1063

Splittings

SylowC1063 ⋊ C4×D4

Subgroups

subgroupG/H
center, FrattiniC22C22×D1063
commutatorC2×C1063C22×C4
Fitting, prime radicalC2×D4×C1063C2
socle, cosocleC22×C1063C23
hypercenterC2×D4D1063
hypocenterC1063C4×D4
LCSG ▷ C2×C1063 ▷ C1063
UCSC1 ◁ C22 ◁ C2×D4

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17008

Conjugacy classes & character table

5330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34016, 109);