Finite Group Databasebeta

C22×Dic2102 #46777719

order33632
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic2102

Splittings

SylowC1051 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D1051
commutator, cosocleC2×C1051C24
FrattiniC2C23×D1051
FittingC22×C4×C1051C2
socle, prime radicalC23×C1051C22
hypercenterC22×C4D1051
hypocenterC1051C22×Q8
LCSG ▷ C2×C1051 ▷ C1051
UCSC1 ◁ C23 ◁ C22×C4

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33632

Conjugacy classes & character table

8420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33632, 186);