Finite Group Databasebeta

C22×Dic2066 #45683170

order33056
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic2066

Splittings

SylowC1033 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D1033
commutator, cosocleC2×C1033C24
FrattiniC2C23×D1033
FittingC22×C4×C1033C2
socle, prime radicalC23×C1033C22
hypercenterC22×C4D1033
hypocenterC1033C22×Q8
LCSG ▷ C2×C1033 ▷ C1033
UCSC1 ◁ C23 ◁ C22×C4

156 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, 186);