Finite Group Databasebeta

D4×Dic1033 #45683093

order33056
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD4×Dic1033

Splittings

SylowC1033 ⋊ C4×D4

Subgroups

subgroupG/H
center, FrattiniC22C22×D1033
commutatorC2×C1033C22×C4
Fitting, prime radicalC2×D4×C1033C2
socle, cosocleC22×C1033C23
hypercenterC2×D4D1033
hypocenterC1033C4×D4
LCSG ▷ C2×C1033 ▷ C1033
UCSC1 ◁ C22 ◁ C2×D4

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16528

Conjugacy classes & character table

5180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33056, 109);