Finite Group Databasebeta

C22×#19153329 #37527216

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

Aliases

direct productC22×#19153329

Splittings

SylowC359 ⋊ C22×SD16

Subgroups

subgroupG/H
centerC23C22⋊D359
commutator, cosocleC4×C359C24
FrattiniC4C23×D359
Fitting, prime radicalC22×D4×C359C2
socleC23×C359D4
hypercenterC22×D4D359
hypocenterC359C22×SD16
LCSG ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11488

Conjugacy classes & character table

3608 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 1322);