Finite Group Databasebeta

C2×#26039955 #37526858

order22976
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#26039955

Splittings

SylowC359 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D359
commutatorC2×C359C22×C8
FrattiniC8C22×D359
FittingC22×C8×C359C2
socleC22×C359C2×C8
prime radicalC23×C359C8
cosocleC8×C359C23
hypercenterC22×C8D359
hypocenterC359C2×M32
LCSG ▷ C2×C359 ▷ C359
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11488

Conjugacy classes & character table

5768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 964);