Finite Group Databasebeta

C2×#26039932 #37526420

order22976
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#26039932

Splittings

SylowC359 ⋊ C2×#100

Subgroups

subgroupG/H
centerC22C22⋊Dic359
commutatorC22×C359C22×C4
FrattiniC2×C4C22×D359
Fitting, prime radicalC22×D4×C359C2
socleC22×C359C22⋊C4
cosocleC2×C4×C359C23
hypercenterC22×D4D359
hypocenterC359C2×#100
LCSG ▷ C22×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5744

Conjugacy classes & character table

3602 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 526);