Finite Group Databasebeta

C22×#10625047 #15686653

order2944
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC22×#10625047

Splittings

FittingC22×C42×C23 ⋊ C2
SylowC23 ⋊ C22×#126

Subgroups

subgroupG/H
centerC24C22×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC22×C42×C23C2
socleC24×C23C23
prime radicalC24×D23C22
hypercenterC22×C42D23
hypocenterC23C22×#126
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C24 ◁ C22×C42

1320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 17766);