Finite Group Databasebeta

C22×Dic1318 #35231359

order21088
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1318

Splittings

SylowC659 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D659
commutator, cosocleC2×C659C24
FrattiniC2C23×D659
FittingC22×C4×C659C2
socle, prime radicalC23×C659C22
hypercenterC22×C4D659
hypocenterC659C22×Q8
LCSG ▷ C2×C659 ▷ C659
UCSC1 ◁ C23 ◁ C22×C4

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21088

Conjugacy classes & character table

5284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21088, 186);