Finite Group Databasebeta

C22×Dic1436 #37527220

order22976
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1436

Splittings

SylowC359 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23D1436
commutator, cosocleC4×C359C24
FrattiniC4C23×D359
FittingC22×C8×C359C2
socle, prime radicalC23×C359D4
hypercenterC22×C8D359
hypocenterC359C22×Q16
LCSG ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22976

Conjugacy classes & character table

5756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 1326);