Finite Group Databasebeta

C2×#27212306 #41003255

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

Aliases

direct productC2×#27212306

Splittings

SylowC421 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D421
commutatorC2×C421C22×C8
FrattiniC8C22×D421
FittingC22×C8×C421C2
socleC22×C421C2×C8
prime radicalC23×C421C8
cosocleC8×C421C23
hypercenterC22×C8D421
hypocenterC421C2×M32
LCSG ▷ C2×C421 ▷ C421
UCSC1 ◁ C2×C8 ◁ C22×C8

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, 964);