Finite Group Databasebeta

C4×Dic2066 #45683096

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

Aliases

direct productC4×Dic2066

Splittings

SylowC1033 ⋊ C4×Q8

Subgroups

subgroupG/H
centerC2×C4C2×D1033
commutatorC2×C1033C22×C4
FrattiniC22C22×D1033
FittingC42×C1033C2
socle, prime radical, cosocleC22×C1033C23
hypercenterC42D1033
hypocenterC1033C4×Q8
LCSG ▷ C2×C1033 ▷ C1033
UCSC1 ◁ C2×C4 ◁ C42

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33056

Conjugacy classes & character table

8276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33056, 112);