Finite Group Databasebeta

C22×Dic1916 #44501172

order30656
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1916

Splittings

SylowC479 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23D1916
commutator, cosocleC4×C479C24
FrattiniC4C23×D479
FittingC22×C8×C479C2
socle, prime radicalC23×C479D4
hypercenterC22×C8D479
hypocenterC479C22×Q16
LCSG ▷ C4×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30656

Conjugacy classes & character table

7676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30656, 1326);