Finite Group Databasebeta

C22×Dic1676 #41001138

order26816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1676

Splittings

SylowC419 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23D1676
commutator, cosocleC4×C419C24
FrattiniC4C23×D419
FittingC22×C8×C419C2
socle, prime radicalC23×C419D4
hypercenterC22×C8D419
hypocenterC419C22×Q16
LCSG ▷ C4×C419 ▷ C2×C419 ▷ C419
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26816

Conjugacy classes & character table

6716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26816, 1326);