Finite Group Databasebeta

C22×D421⋊C8 #41003911

order26944
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D421⋊C8
unambiguous semidirect productD421⋊(C22×C8)

Splittings

derived, SylowC421 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#13132997
commutator, hypocenterC421C23×C8
FrattiniC2C23×#13132997
FittingC22×C4×C421C4
socleC23×C421C2×C4
prime radicalC23×D421C4
cosocleDic421C24
LCSG ▷ C421
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13472

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 1620);