Finite Group Databasebeta

C22×#16840654 #30623840

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16840654

Splittings

SylowC61 ⋊ C22×#347

Subgroups

subgroupG/H
centerC22×C4C4×#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC22×C42×C61C4
socleC23×C61#97
prime radicalC24×C61M16
cosocleC2×#92418C24
hypercenterC22×C42#6923
hypocenterC61C22×#347
LCSG ▷ C4×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1048 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1113395);