Finite Group Databasebeta

C4×Dic2122 #46800596

order33952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic2122

Splittings

SylowC1061 ⋊ C4×Q8

Subgroups

subgroupG/H
centerC2×C4C2×D1061
commutatorC2×C1061C22×C4
FrattiniC22C22×D1061
FittingC42×C1061C2
socle, prime radical, cosocleC22×C1061C23
hypercenterC42D1061
hypocenterC1061C4×Q8
LCSG ▷ C2×C1061 ▷ C1061
UCSC1 ◁ C2×C4 ◁ C42

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33952

Conjugacy classes & character table

8500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33952, 112);