Finite Group Databasebeta

C2×#26039971 #37526896

order22976
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#26039971

Splittings

SylowC359 ⋊ C2×#117

Subgroups

subgroupG/H
centerC23C22×D359
commutatorC2×C359C23×C4
FrattiniC22C23×D359
FittingC2×C22⋊C4×C359C2
socleC23×C359C23
prime radicalC24×C359C22
cosocleC22×C359C24
hypercenterC2×C22⋊C4D359
hypocenterC359C2×#117
LCSG ▷ C2×C359 ▷ C359
UCSC1 ◁ C23 ◁ C2×C22⋊C4

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11488

Conjugacy classes & character table

3620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 1002);