Finite Group Databasebeta

C2×#27212305 #41003254

order26944
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27212305

Splittings

FittingC2×C16×C421 ⋊ C2
SylowC421 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D421
commutatorC2×C421C22×C8
FrattiniC8C22×D421
FittingC2×C16×C421C2
socleC22×C421C2×C8
prime radicalC22×D421C8
cosocleC8×C421C23
hypercenterC2×C16D421
hypocenterC421C2×M32
LCSG ▷ C2×C421 ▷ C421
UCSC1 ◁ C2×C8 ◁ C2×C16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13472

Conjugacy classes & character table

6760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 963);