Finite Group Databasebeta

C22×(C2×D359)⋊C4 #37526890

order22976
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D359)⋊C4

Splittings

FittingC23×C4×C359 ⋊ C2
SylowC359 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D359
commutatorC2×C359C23×C4
FrattiniC22C23×D359
FittingC23×C4×C359C2
socleC24×C359C22
prime radicalC24×D359C2
cosocleC22×C359C24
hypercenterC23×C4D359
hypocenterC359C22×C22⋊C4
LCSG ▷ C2×C359 ▷ C359
UCSC1 ◁ C24 ◁ C23×C4

674 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, 996);