Finite Group Databasebeta

C22×Dic359⋊C4 #37526893

order22976
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×Dic359⋊C4

Splittings

SylowC359 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D359
commutatorC2×C359C23×C4
FrattiniC22C23×D359
FittingC23×C4×C359C2
socle, prime radicalC24×C359C22
cosocleC22×C359C24
hypercenterC23×C4D359
hypocenterC359C22×C4⋊C4
LCSG ▷ C2×C359 ▷ C359
UCSC1 ◁ C24 ◁ C23×C4

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22976

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, 999);