Finite Group Databasebeta

C22×Dic1756 #43244381

order28096
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1756

Splittings

SylowC439 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23D1756
commutator, cosocleC4×C439C24
FrattiniC4C23×D439
FittingC22×C8×C439C2
socle, prime radicalC23×C439D4
hypercenterC22×C8D439
hypocenterC439C22×Q16
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28096

Conjugacy classes & character table

7036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 1326);