Finite Group Databasebeta

C2×#26039946 #37526473

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

Aliases

direct productC2×#26039946

Splittings

SylowC359 ⋊ C2×#106

Subgroups

subgroupG/H
centerC23C22⋊D359
commutatorC4×C359C22×C4
FrattiniC2×C4C22×D359
FittingC2×C4⋊C4×C359C2
socle, prime radicalC23×C359D4
cosocleC2×C4×C359C23
hypercenterC2×C4⋊C4D359
hypocenterC359C2×#106
LCSG ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22976

Conjugacy classes & character table

3608 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 579);