Finite Group Databasebeta

C2×D421⋊C16 #41003894

order26944
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×D421⋊C16
unambiguous semidirect productD421⋊(C2×C16)

Splittings

derived, SylowC421 ⋊ C22×C16

Subgroups

subgroupG/H
center, hypercenterC2×C8#13132997
commutator, hypocenterC421C22×C16
FrattiniC4C22×#13132997
FittingC2×C8×C421C4
socleC22×C421C2×C8
prime radicalC22×D421C8
cosocle#16809890C23
LCSG ▷ C421
UCSC1 ◁ C2×C8

98 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, 1603);