Finite Group Databasebeta

C22×#19153328 #37527215

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

Aliases

direct productC22×#19153328

Splittings

FittingC22×Q8×C359 ⋊ C2
SylowC359 ⋊ C22×SD16

Subgroups

subgroupG/H
centerC23C22⋊D359
commutator, cosocleC4×C359C24
FrattiniC4C23×D359
FittingC22×Q8×C359C2
socleC23×C359D4
prime radicalC22×D1436C2
hypercenterC22×Q8D359
hypocenterC359C22×SD16
LCSG ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

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, 1321);